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POLYPHASE 


ELECTRIC CURRENTS 

AND 

ALTERNATE-CURRENT MOTORS 


SILVANUS P. THOMPSON 

r\SC„ B.A., F.R.S. 


PRINCIPAL OF, AND PROFESSOR OF PHYSICS IN, THE CITY AND GUILDS OF 
LONDON TECHNICAL COLLEGE, FINSBURY 





NEW YORK 

AMERICAN TECHNICAL BOOK COMPANY 
45 Vesey Street 
1807 



■f K /^ 1 

T5" 

% 1 



COMPOSITION AND ELECTROTTPING 
BY 

Phillips & Casey, Rouses Point, N. Y 0 


V 




Braumvorth, Minm and Barber 
Printers and Binders. 
Brooklyn, N. V 


PREFACE. 


When the course of four Lectures on the subject of Poly¬ 
phase Currents, delivered by the author at the Technical 
College, Finsbury, in the autumn of 1894, was completed, 
representations were made Ity persons who had attended the 
Lectures, and by others, to induce him to publish them in 
permanent form. 


In preparing the lectures for the press a good deal of 
matter has been added. No attempt has been made either to 
preserve the colloquial form of the discourses or to give to 
them any pretence to literary style. They are put together 
in their present shape for the use of students and engineers, 
and introductory matter has been added to make the rela¬ 
tions of polyphase currents to ordinary single-phase currents 
more clear. In all this work the author has been aided by 
Mr. Miles Walker, whose assistance is willingly acknowledged, 
and on whom the task of reducing to written form much of 
the work has devolved. The graphic method of treating 
monophase motors, on pp. 165 to 169, is due to Mr. Walker. 


The author is also indebted to various firms and designers 
for valuable information afforded as to recent progress and 
modern types of machine, and he desires to express his thanks 



vi Polyphase Electric Currents . 

to the following : the Allgemeine Elektricitats-Gesellschaft, 
of Berlin ; the Helios Company, of Cologne; the Elektricitats- 
Aktiengesellschaft (Messrs. Schuckert & Co.), of Niirnberg; 
the Oerlikon Maschinen-Fabrik (and to Mr. Emil Kolben) of 
Ziirich; and most of all to Brown, Boveri & Co. (and to 
Mr. C. E. L. Brown), of Baden, Switzerland. 

A full Bibliography of the subject of Polyphase Currents 
and Induction Motors has been appended at the end of the 
volume. 


S. P. T. 


CONTENTS. 


CHAPTER PAGE 

I. Polyphase Generators. 1 

II. Combinations of Polyphase Currents. 43 

III. Properties of Rotating Magnetic Fields. 69 

IV. Early Development of Rotary-Field Motors.. 84 

V. Structure of Polyphase Motors. Ill 

VI. Elementary Theory of Polyphase Motors .. . 134 

VII. Analytical Theory of Polyphase Motors. 146 

VIII. Monophase Motors. 153 

IX. Miscellaneous Alternate-Current Motors.... 170 

X. Polyphase Transformers. 176 

XI. Measurement of Polyphase Power. 187 

XII. Notes on Design of Polyphase Motors. 190 

XIII. Mechanical Performance of Polyphase Motors 197 

XIV. Some Examples of Modern Polyphase Motors. . 210 

XV. Distribution of. Polyphase Currents from 

Stations. 217 

APPENDIX 

I. Bibliography. 225 

II. Schedule of British Patents on Polyphase 

Motors. 242 

Index. . 245 


Plate 1. Tw t o-Phase, Six Horse-power Motor. 263 

« II. Three-Phase, One Hundred Horse-power 

Motor. 265 











































■ 





. 











. 











- 



































































POLYPHASE 


ELECTRIC CURRENTS AND ALTERNATE- 
CURRENT MOTORS. 

CHAPTER I. 

POLYPHASE GENERATORS. 

INTRODUCTORY REMARKS. 

No apology is needed for devoting special attention at the 
present time to the subject of polyphase electric currents. 
There seems to be no doubt that in the problem of the electric 
transmission of power a very important part will, in the 
future, be played by alternating currents combined in systems 
of two or three different phases. Already a number of 
examples exist; and some very large works are now in course 
of construction. The undoubted advantages possessed by 
polyphase systems over either (a) continuous current systems, 
or ( b ) ordinary single-phase alternate currents, for the special 
service of power transmission, are beyond question ; but it 
remains to be seen how far the complications thereby inevi¬ 
tably introduced are, in practice, sufficiently great to militate 
against polyphase distribution for the purpose of general 
electric lighting supplies. 

The comparative novelty of polyphase methods, and the 
circumstance that the greater part of that which has already 
been achieved has been done in foreign countries, are reasons 
why the topic should receive some attention from English 
engineers. 




2 


Polyphase Electric Currents . 


In these pages the subject will be dealt with under the 
following subdivisions :—Generators for Polyphase Currents ; 
the Properties of the Rotatory Magnetic Field, with some 
account of its historical development; the Theory, Construc¬ 
tion and Performance of Polyphase Motors; the Theory and 
Construction of Motors operated by ordinary single-phase 
Alternate Currents ; together with some account of Polyphase 
Transformers, and of the measurement of power in polyphase 
systems. 

ALTERNATE CURRENTS. 

It will be assumed at the outset that we are already 
acquainted with the general principles of alternate-currents, 
and with the general features 1 of alternators or alternate- 
current generators. 

Nevertheless, a recapitulation of the main points about 
alternate currents may be useful as a preliminary. 

Faraday’s discovery of the induction of currents in wires 
by moving them across a magnetic field, so as to cut the 

magnetic lines, suggested 
the construction of mag¬ 
neto-electric machines to 
generate currents by 
mechanical power. If a 
coil of suitable form is 
placed, as in Fig. 1, be¬ 
tween the poles of a 
magnet, and spun around 
a longitudinal axis, it will 
have currents generated 
in it which at each semi¬ 
revolution die away and 
then reverse. In the 
figure the coil of wire is supposed to be so spun that the 
upper portion comes towards the observer. In that case, the 

1 For a simple outline of the subject see Chapters IX. and X. of the 1894 
edition of the author’s Elementary Lessons in Electricity and Magnetism; 
or, for a fuller account, consult the author’s larger treatise on Dynamo- 
electric Machinery. 


















Polyphase Generators . 


3 


arrows show the direction of the induced currents delivered 
to the circuit through the agency of two contact rings (or 
slip-rings) connected respectively to the ends of the coils. In 
the position shown, the current will be delivered to the left- 
hand ring, and returns from the circuit to the right-hand ring; 
but half a turn later it will be flowing to the right-hand ring 
and returning from the circuit back to the left-hand ring. 
Fig. 1 is, in fact, a primitive form of alternator, generating a 
simple periodically reversed or alternating current ; and is, in 
fact, the kind of alternator known as a “ magneto-ringer,” 
used for bell service in telephone sets. In alternate current 
working, the current is rapidly reversed, rising and falling 
in a set of pulses ; the electric currents being set oscillating 
forwards and backwards through the line and around the 
circuit with great rapidity—scores or hundreds of times a 
second—under the influence of a rapidly reversing electro¬ 
motive force. As is well known, the properties of alternate 
currents differ somewhat from those of continuous currents. 
They are affected not only by the resistance of the circuit, but 
also by its electro-magnetic inertia or self-induction (in other 
words, by the magnetic field which it sets up around itself), 
the inductance of the circuit having a choking effect on the 
alternate currents, diminishing their amplitude, retarding 
their phase, and smoothing down their ripples. 

In Fig. 1 the revolving armature was a simple coil, and 
the magnet of simple 2-pole horse-shoe form. But for reasons 
mentioned later, the majority of alternate-current generators 
are multipolar. Fig. 2 illustrates a frequent form introduced 
by the Westingliouse Company, having a multipolar field- 
magnet consisting of a number of radial poles pointing 
inwards, whilst the revolving coils are grouped upon the 
periphery of a drum or cylinder built up of iron core-disks. 

In order to study the combinations of wires, we must 
devote a moment to the directions of the currents induced in 
them. 

Consider first Fig. 3, which is a partial sketch of a 4-pole 
machine laid on its sides. The core, to receive hereafter its 
appropriate winding, lies between four poles of alternate 


4 


Polyphase Electric Currents . 

polarity. If a copper rod a b is placed parallel to the axis 
to represent one of the armature conductors, and is supposed 
to move along the gap-space right-handedly past the S pole, 
it will cut the magnetic lines entering that pole. By the 



Fig. 2.—The Westinghouse Co.’s Alternator (Single-phase). 

rule given below, the induced electromotive-force in it will 
be upwards. Another conductor c d passing the N pole will 
have induced in it a downward electromotive force. If one 
was to attempt in a picture such as this to show twenty or 


























































Polyphase Generators . 


5 


more conductors and their respective connections, the drawing 
would be unintelligible. Accordingly we have to imagine 
ourselves placed at the centre, and the panorama of the four 
poles around us to be then laid out flat, as in Fig. 4. It will 
be noticed that the faces of the N and S poles are shaded 
obliquely for distinction. 

The oblique lines are used for the following purpose. If 
instead of the line a b (representing a conductor), a narrow 
slit in a piece of paper were laid 
over the drawing of the pole-face, 
and moved as the dotted arrows 
show towards the right, the slit in 
passing over the oblique lines will 
cause an apparent motion in the 
direction in which the current 
tends in reality to flow. It is easy 
to remember which way the oblique 
lines must slope; for those on a 
north pole-face slope parallel to 
the oblique bar of the letter N. 

Now in an actual machine there are many armature con¬ 
ductors spaced symmetrically around, and these have to be 
grouped together by connecting wires, or pieces. In the case 



Fig. 3.—Sketch of Four- 
pole Field. 



Fig. 4 . —Four-pole Field developed Flat. 


of ring-wound armatures the connecting conductor goes 


























6 


Polyphase Electric Currents . 

through the interior of the ring-core, thus constituting a spiral 
winding . When we go on to those cases in which the winding 
is entirely exterior to the core, as for drum armatures and disk 
armatures, we find that there are two distinct modes of pro¬ 
cedure, which we may respectively denote as lap-winding and 
wave-winding. The distinction arises in the following manner. 
Since the conductors that are passing a north pole generate 
electromotive forces in one direction, and those that are 
passing a south pole generate electromotive forces in the 
opposite direction, it is clear that a conductor in one of these 
groups ought to be connected to one in a nearly corre¬ 




sponding position in the other group, so that the current may 
flow down one and up the other in agreement with the direc¬ 
tions of the electromotive forces. So after having passed 
down opposite a north pole face, the conductor may be con¬ 
nected to one that passes up opposite a south pole face, and 
the winding evidently may be arranged either to lap back, or 
to zigzag forward. 

This distinction between lap-windings and wave-windings 
as applied to alternate current machines, is illustrated in 
Figs. 5 and 6. Fig. 5 represents an 8-pole alternator with 
lap-winding, each “ element ” or set of loops extending across 
























































































Polyphase Generators. j 

the same breadth as the 44 pitch ” or distance from centre to 
centre of two adjacent poles. Only 24 conductors have been 
drawn; and it will be noticed that the successive loops are 
alternately right-handed and left-handed. In Fig. 6 is shown 
the same alternator with a wave-winding. The electromotive 
force of the two machines would be precisely the same; the 
choice between the two methods of connecting is here purely 
a question of mechanical convenience in construction and cost. 
In cases where the armature revolves, the beginning and end 
of the winding are connected to two slip-rings, which in these 
, developed drawings are represented by two parallel lines. 

Returning to the simple revolving coil represented in 
Fig. 1, we have seen above how the coil, by cutting the lines 
of the magnetic field, sets up periodic electromotive forces, 
which change at every half-turn, giving rise to alternate 
currents. In each whole revolution there will be an electro¬ 
motive force which rises to a maximum and then dies away, 
followed immediately by a reversed electromotive force, 
which also grows to a maximum and then dies away. 
The wave-form depicted in Fig. 7 serves to illustrate this. 



Fig. 7.—Curve of Induced Electromotive Force in an Ordinary or 
Single-phase Alternator. 

The heights of the curve above the horizontal line represent 
the momentary values of the electromotive forces: the depths 
below, in the second half of the curve, represent the inverse 
electromotive forces that succeed them. Each such complete 
set of operations is called a period , and the number of 
















8 


Polyphase Electric Currents. 

periods accomplished in a second is called the frequency or 
periodicity of the alternations, and is symbolized by the 
letter n. In 2-pole machines n is the same as the number i 
of revolutions per second; but in multipolar machines n is 
greater, in proportion to the number of pairs of poles. 
Thus, in an 8-pole field with 4 north poles and 4 south 
poles around a centre there will be produced 4 complete 
periods in one revolution. If the machine revolves 15 times 
a second (or 900 times a minute) there will be 60 periods a 
second, or the periodicity will be 60. By revolving in a 
uniform field the electromotive forces set up are proportional 
to the sine of the angle through which the coil has turned 
from the position in which it lay across the field. If in this 
position the flux of magnetic lines through it were |SJ, and 
the number of spirals in the coil that enclose the N lines be 
called S, then it can be shown that the value of the induced 
electromotive force at any time t when the coil has turned 
through angle 0 = 2 r, n t will be 

E# = 2 7T n S N sin 0 ~ 10 8 , 
or, writing D for 2 * n S |\J / 10 8 , we have 
E o — D sin 0. 

In actual machines the magnetic fields are not uniform, 
nor the coils simple loops, so the periodic rise and fall of the 
electromotive forces will not necessarily follow a simple sine | 
law. The form of the impressed waves will depend on the , 
si iape of the polar faces, and on the form and breadth of the coils. 
But in most cases we are sufficiently justified in assuming 
that the impressed electromotive force follows a sine law, so 
that the value at any instant may be expressed in the above 
form, where D is the maximum value or amplitude attained 
by E, and 0 an angle of phase upon an imaginary circle of 
reference. Consider a point P revolving clockwise round a 
circle (Fig. 8). If the radius of this circle be taken as unity, 

P M will be the sine of the angle 0 , as measured from 0°. Let 
the circle be divided into any number of equal angles, and let 
the sines be drawn similarly for each. Then let these sines 





9 


Polyphase Generators. 

be plotted out at equal distances apart along the horizontal 
line, as in Fig. 8, giving us the sine curve. 

In Fig. 8 one revolution of P around the circle of reference 
corresponds to one complete alternation or cycle of changes. 
The value of the electromotive force (which varies between 


Fig. 8. 

-f D and - D as its maximum values) may be represented 
at any moment either by the sine P M or by projecting P on 
to the vertical diameter, giving O Q. As P revolves, the 
point Q will oscillate along the diameter. 

The currents which result from these periodic or alter¬ 
nating electromotive forces are also periodic and alternating ; 
they increase to a maximum, 
then die away and reverse in 
direction, increase, die away, 
and then reverse back again. 

If the electromotive force 
completes 100 such cycles or 
reversals in a second, so also 
will the current. 

There is yet another way 
of representing periodic varia¬ 
tions of this kind—namely, by 
a diagram akin to that used 
by Zeuner for valve-gears. 

Let the outer circle (Fig. 9) 
be, as before, a circle of reference around which P revolves. 
Upon each of the vertical radii describe a circle. Then the 



Fig. 9. 



























IO Polyphase Electric Currents . 

lengths such as O Q, cut off from the radii, represent the 
corresponding values of the sine of the angle. If a card with 
a narrow slit cut radially in it were made to revolve over this 
figure, the intersection with the two inner circles would show 
the varying electromotive forces in various positions. 

The reader who desires to pursue the graphic study of 
these matters further should consult the excellent treatise of 
Prof. Fleming, 1 or that of Mr. Blakesley, 2 and sundry papers 
by Mr. Kapp. 3 

An application of this construction to a 3-phase system is 
shown in Fig. 10, where the three lines 120° from one another 
are supposed to revolve behind the two 
A circular openings. The lengths of the 

® three lines visible at any instant represent 
respectively the values of the 3 electro¬ 
motive forces of the 3 currents. 

The ordinary measuring instruments 
for alternate currents, such as electro¬ 
dynamometers, Cardew voltmeters and 
electrostatic voltmeters, do not measure* 
Fig. 10. the arithmetical average values of the 

amperes or volts. The readings of these 
instruments, if first calibrated by the use of continuous currents, 
are the square roots of the means of the squares of the values 
They measure what are called virtual amperes or virtual volts 
The mean which they read (if we assume the currents and vol¬ 
tages to follow the sine law of variation) is equal to 0*707 of 
the maximum values, for the average of the squares of the sine 
taken over either 1 quadrant or a whole circle is i ; hence 
the square-root-of-mean-square value is equal to 1-r- V 2 times 
their maximum value. If a voltmeter is placed on an alter¬ 
nating circuit in which the volts are oscillating between 
maxima of + 100 and — 100 volts, it will read 70*7 volts ; 
and 70*7 volts continuously applied would be required to pro- 

1 Fleming, The Alternate Current Transformer, London, 1889. 

2 Blakesley, Alternating Currents of Electricity , London, 1889. 

8 Kapp on ‘ Alternate Current Machinery,’ Proc. Inst. Civil Engineers , 
1889, pt. iii. 









Polyphase Generators . 


ii 


duce an equal reading. If an alternate-current ampere meter 
reads 100 amperes, that means that the current really rises to 
+ 141*4 amperes and then reverses to - 141*4 amperes; 
but the effect is equal to that of 100 continuous amperes ; 
and therefore such a current would be described as 100 virtual 
amperes. 

Alternating currents do not always keep step with the alter¬ 
nating volts impressed upon the circuit. If there is inductance 
in the circuit the currents will lag ; if there is capacity in the 
circuit they will lead in phase. Fig. 11 illustrates the lag 
produced by inductance. The curve marked V represents the 
alternating volts ; that marked C is the current curve. Dis¬ 
tances measured from O along the horizontal line represent 
time. The impulses of current, represented by the blacker 



line, occur a little later than those of the volts. But in¬ 
ductance has another effect of more importance than any 
retardation of phase; it produces reactions on the electro¬ 
motive force, choking the current down. While the current 
is increasing in strength the reactive effect of inductance 
tends to prevent it rising. To produce a current of 40 am¬ 
peres in a resistance of li ohms would require — for 
continuous currents — an E.M.F. of 60 volts. But an 
alternating voltage of 60 volts will not be enough if there 
is inductance in the circuit reacting against the voltage. 
The matter is complicated by the circumstance that the 
reactive impulses of electromotive force are also out of step: 
they are, in fact, exactly a quarter period behind the current. 
If an alternate current of C (virtual) amperes is flowing with 
a frequency of n cycles per second through a circuit of induct • 




12 


Polyphase Electric Currents . 

ance L, the reactive electromotive force 1 will be 2 n n L C 
(virtual) volts. If, for example, L = 0*002 henry, n = 50 
periods per second, and C = 40 amperes, the reactive elec¬ 
tromotive force will be 25*1 volts. Now, if we wish to drive 
the 40 (virtual) amperes not only through the resistance of 
1 1 ohms but against this reaction, we shall require more than 
60 volts. But we shall not require 60 + 25*1 volts, since the 
reaction is out of step with the current. Ohm’s law is no 
longer adequate. To find out what volts will be needed we 
have recourse to geometry. 



Plot out (Fig. 12) the wave-form O A b d, to correspond to 
the volts necessary to drive the current through the resistance 
if there were no inductance. The ordinate a A may be taken 
to scale as 60. This we may call the current curve. Then 

1 This is calculated as follows. By definition, L, the coefficient of self-in¬ 
duction, or inductance, represents the amount of self-enclosing of magnetic 
lines by the circuit when the current has unit value ; hence when current 
has value C the actual self-induction is C times L. And, as the self-induced 
electromotive-force is proportional to the rate of change of this quality, we 
may write E = L . d C / d t. Now C is assumed to be a sine function of 
the time having instantaneous value C 0 sin 2 tt n t ; where C 0 is the maximum 
value of C. Differentiating this with respect to time we get dCdt = 2Trn 
C 0 cos27t nt . The “virtual” values of cosine and sine being equal we have 
for E the value 2 tt n L 0, but differing by £ period from the current in 
phase. 










Polyphase Generators . 


13 


plot out the curve marked — p L C to represent the volts 
needed to balance the reaction of the inductance. Here p is 
written for 2 xn. The ordinate at O is 25T : and the curve 
is shifted back one-quarter of the period: for when the current 
is increasing at its greatest rate, as at O, the self-inductive 
action is greatest. Then compound these two curves by 
adding their ordinates, and we get the dotted curve, with its 
maximum at V. This is the curve of the volts that must be 
impressed on the circuit in order to produce the current. It 
will be seen that the current curve attains its maximum a 
little after the voltage curve. The current lags in phase 
behind the volts. If O d is the time of one complete period, 
the length v a will represent the 
time that elapses between the 
maxima of volts and amperes. In 
Fig. 13 the same facts are repre¬ 
sented in a revolving diagram of 
the same sort as Fig. 9. The line 
O A represents the working volts 
R X C, whilst the line A D at 
right angles to O A represents the 
self-induced volts p L C. Com¬ 
pounding these as by the triangle 
of forces, we have as the impressed 
volts the line O D. The projec¬ 
tions of these three lines on a vertical line while the diagram 
revolves around the centre O give the instantaneous values 
of the three quantities. The angle A O D, or 0, by which 
the current lags behind the impressed volts, is termed the 
angle of lag. However great the inductance or the fre¬ 
quency, angle 0 can never be greater than 90°. If O A is 60 
and AD is 25T, O D will be 65 volts. In symbols, the 
impressed volts will have to be such that E 2 =(R L C)". 

This gives us the equation :— 

C =- -- 

V R a +/L 2 

The denominator which comes in here is commonly called 

the impedance. 







14 Polyphase Electric Currents. 

In Figs. 14 and 15 the angle of lag is seen to be such that 
tan ^ =p LC/RCor=^L/R. And it is evident that the 
effect of the inductance is to make the circuit act as if its 

resistance, instead of being R, was increased to 4 /R 2 -\-p L . 
In fact, the alternate current is governed, not by the resistance 




R 

Jig. 14. Fig. 15. 

of the circuit, but by its impedance. At the same time, the 
current is lagging as if the angle of reference were not 0 but 
0— 0 , so that the equation for the instantaneous values of C, 
when E = D sin 0 , is 

_D sin (0 — 0) 

VR* + p*l)' 




This is Maxwell’s law for periodic currents as retarded by 
inductance. As instruments take no account of phase but 
give virtual values, the simpler form preceding is usually 
sufficient. 

The effect of capacity introduced into an alternate-current 
circuit, as by the introduction of a condenser, is to produce a 
lead in the phase of the current. For when the volts are 


C_ 

PK 




changing most quickly (as at O in Fig. 11) from negative to 
positive, the current running into the condenser is greatest; 
the maximum point of the current curve being thus nearly 

















i 5 


Polyphase Generators. 

90° in advance of that of the curve of volts. The reaction 
of a condenser, instead of tending to prolong the current, 
tends to drive it back, and cause it to reverse its direction 
before the volts have reversed. The reactance is therefore 
written as — 1 /joK, and the angle 0 will be such that 
tan f =-l/pKR. The impedance will be |/R 2 + 1 / p 2 K 2 . 

If both inductance and capacity are present, 
tan <t> = (p L — 1 / p K) / R, 
the reactance will be 

Jp L —1/jpK; 

and the impedance 

4 / R 2 + (pL — 11 p K) 2 . 

Since capacity and inductance produce opposite effects, 
they can be used to neutralize one another. They exactly 
balance if L = l/p 2 K. In that case the circuit is non- 
inductive and the currents simply obey Ohm’s law. 

It will be seen that if in a circuit there is little resistance 
and much reactance, the current will depend almost exclu¬ 
sively on the reactance. For example, if p (= 2 xn) were, 
say, 1000 and L = 10 henries, while R was only 1 ohm, the 
resistance part of the impedance would be negligible, and the 
law would become 



Self-induction coils with large inductance and small resistance 
are sometimes used to impede alternate currents, and are 
called choking coils , or impedance coils. 

If the current were led into a condenser of small capacity 
(say K = microfarad, then 1 Ip K = 10,000), the current 
running in and out of the condenser would be governed only 
by the capacity and frequency, and not by the resistance, and 
would have the value— 

C = EpK. 

The measurement of alternate-current power needs careful 
consideration. If to measure the power supplied to a motor 




16 Polyphase Electric Currents . 

or other part of an alternate current circuit, we measure 
separately with an amperemeter and voltmeter the amperes 
and volts, and then multiply together the readings, we obtain 
as the apparent watts a value often greatly in excess of the 
true watts , owing to the difference in phase, of which the 
instruments take no account. The true power (watts) is in 
reality W = CV cos 0, where C and V are the virtual values, 
and 0 the angle of lag. But the latter is usually an unknown 
quantity. Hence recourse must be had to a suitable watt¬ 
meter; the usual form being an electrodynamometer specialty 
constructed so that the high-resistance circuit in it shall be 
non-inductive. 

Whenever the phase-difference (whether lag or lead) is 
very large, the current, being out of step with the volts, is 
almost wattless. This is the case with currents flowing through 
a choking-coil or into a condenser, if the resistances are 
small. 


POLYPHASE GENERATORS. 

We are now in a position to consider the question of poly¬ 
phase generators. Briefly, the principle of polyphase working 
consists in providing the armature of the alternator with coils 
grouped in sets of two, three, or more, which come successively 
into action in each period. 

Up to this point it has been assumed that the field-magnets 
of the alternator are stationary, whilst the armature revolves. 
But this is not necessarily so. Indeed, in the majority of 
modern alternators, whether single-phase or polyphase, the 
reverse arrangement is adopted. The field-magnets revolve, 
whilst the armature is fixed. The preference given to this 
arrangement arises from the greater facility with which insu¬ 
lation of the windings can be insured if the armature is 
stationary ; and this becomes of great importance when, for the 
purpose of transmission to a distance, high voltages are used. 

Suppose, then, we consider a very simple case of a stationary 
armature a ring with two coils wound upon it at opposite 
parts—and a revolving field-magnet of simple bipolar form. 







T 7 


Polyphase Generators. 

Here in Fig. 18 two such elementary machines are repre¬ 
sented as connected by a couple of lines for a transmission 
of power, one serving as generator, and requiring to be driven 
by a steam engine or turbine, the other running as a syn¬ 
chronous motor. As is well known, such a motor will not he 
self-starting. It must be started by hand or in some other 
way, and run up to speed before it is thrown into the circuit; 
and when so started, runs in absolute synchronism with the 
generator, its electromotive force being in almost exact op¬ 
position of phase. 



Fig. 18.— Transmission from a simple Single-phase Alters top 
to a simple Synchronous Motor. 


Some of the very earliest alternators—those of Lontin 
and Gramme, had revolving multipolar field-magnets with 
external stationary armatures. Gramme’s alternators were 
built about 1877 for the purpose of supplying alternate 
currents for working Jablochkoff candles. The diagram. 
Fig. 19, of this machine shows that it had eight revolving 
poles, alternately north and south poles The armatures, 
having a ring core of laminated iron, received the windings of 
copper wire in which the alternating currents were to be 
induced. Now it was found (as will be considered presently) 
that it was no use making the individual coils very broad. In 










i8 


Polyphase Electric Currents. 


fact, the closer together the coils in any one group can be 
huddled together, the more effective are they. Hence, in this 
machine had there been only eight narrow coils—one opposite 
each pole—there would have been much idle space on the 
machine. Gramme, therefore, filled up the idle space with 
other coils. The sections of the winding of this machine 
were, in fact, four times as numerous as the poles, and might 
have been coupled to feed four separate circuits. It is clear 
that the revolving poles would come past the four adjacent 
sections successively, so that the four alternating currents 



generated would differ in phase from one another. Gramme 
knew or discovered that it would not do to join all the coils 
together. Ho only joined together those that at any one 
instant were opposite the poles. So there were four separate 
circuits each consisting of eight coils joined up in series. And 
these four separate windings were led off to four entirely 
separate circuits, each supplying a number of Jabloclikoff 
candles with current. Gramme’s alternator was unquestion¬ 
ably a polyphase generator; but there is not the slightest 
evidence that he at any time attempted to combine the 
currents of separate phases for any useful purpose, or that he 














Polyphase Generators . 


*9 

knew that they could be so combined. On the contrary, he 
always kept the circuits separate because the several currents 
in them were not in phase with one another. 

The large two-phase alternators at Paddington, designed 
by the late Mr. Gordon, have been running ever since 1883. 

In 1886 F. Wynne proposed a system of distributing cir¬ 
cuits, “ the alternating currents in which are so ordered that 
while the rate of alternation is the same in all of them, the 
instant at which the alternation takes place is different.” 

It may be remarked, in passing, that in every type of 
alternator there will be idle space between the groups of coils 
if they are wound for single-phase working. Returning to 



Fig. 20.—Illustration of Two-phase Transmission. 


Fig. 18, we note that between the two coils on the ring there 
was idle space which might advantageously be filled up. 
Suppose, then, that beside the two coils A A' on each machine 
there are wound other two B B' between the former pair, and 
that these are connected through a new pair of lines b b and 
b' b', Fig. 20. It is clear that a second set of alternating 
currents will be set up in B B' which will be exactly a quarter- 
period in phase behind those in A A'. In fact, the two 
currents will be represented by the two waves of Fig. 21. 
The electromotive force in A will be greatest just when the 
pole of the magnet is passing its middle, for at that instant 
















20 


Polyphase Electric Currents. 

the rate of change in the magnetization of its core is a maxi¬ 
mum. And the maxima for the B coils will correspond to 
the zeros for the A coils and vice versa. Two alternate 
currents differing in this manner by a quarter period are said 
to be “in quadrature.” The currents in the A coils of the 
motor, tending to drag forward the pole of the field-magnet, 
will not have died down to zero before the currents in the 
B coils will have already begun ; so that there is no dead- 
point. It is easy to see that in the motor there will be 
a regular displacement around the ring of the resultant 
poles. At the moment when the current in A A' is at a 
maximum that in B B' will be zero, and the magnetizing 


AD a 



Fig. 21.—Two Alternate Currents differing by a 
Quarter Period. 

action of A A' will be to produce two double-poles in the ring 
at opposite ends of a diameter right under the middle of the 
B B' coils. As the current in A A' dies down that in B B' 
begins and increases, and therefore shifts the pole forward. 
When the currents in A A' and B B' have become equal, A 
and B will act together as one coil, while A ; and B will act 
together as another coil, the resulting poles lying now between 
B and A' on the right and between IV and A on the left. When 
the B current is at its maximum the poles will lie right under 
the middle of the A coils. A pair of travelling poles are 
therefore produced in the motor ring by the currents coming 
from the generator, and the magnet in the motor is continually 
trying to catch up these travelling poles. There are no dead- 












Polyphase Generators. 


21 


points. The motor will be self-starting if its magnet is not 
too powerful, and will run up in speed until synchronism is 
attained. This is, indeed, the great advantage of polyphase 
currents—they enable motors to be self-starting. But 
this is not by any means the sole advantage of polyphase 
geneiatois. We see that they enable a machine to be made 
which by doubling merely the quantity of copper in the arma¬ 
ture will serve as a machine of double power. 1 It will take 
twice as much horse-power to drive, and will give out twice 
as much horse-power. But it will not cost twice as much, 
nor will it take up any more space. It is worthy of remark, 
too, that the armature reactions for a two-phase generator are 
no greater than those of the same machine used as a single¬ 
phase alternator. 



Fig. 22.—A Three-phase Generator. 


Suppose that, instead of using two separate groupings of 
coils we had used three, as indeed Gramme employed in some 
of his smaller machines. We should then have three currents 
in three separate successive phases. If these were grouped 
as in Fig. 22, we might join up the A coils together into one 
circuit (the coils being wound or connected alternately right- 
handedly and left-handedly) ; the B coils being similarly 
joined up into a second circuit, and the C coils being joined 
into a third. It is clear that in each set the electromotive- 
forces would rise and fall in regular succession, and that the 

1 H. Goerges : “ The Comparative Output of the Continuous, Alternating 
and Drelistrom Armature,” Elektrotechnische Zeitschrift, vol. xiii. p. 236. 
Herr von Dobrowolsky mentioned in the discussion of the above paper, a 
multipolar continuous-current machine which gave 11,000 watts ; the same 
field magnet with a three-phase armature gave an output of 30,000 watts. 










22 Polyphase Electric Currents . 

electromotive force in B would not rise to its maximum until 
after that in A had passed its maximum and was falling. In 
fact, the differences of phase might be represented by the 
three curves of Fig. 23. Since the angular distance around 
the machines from one north pole to the next north pole 
corresponds to one whole “ period ” (p. T), or to one complete 
revolution of 360° on the imaginary circle of reference 
(Fig. 8), we see that these three currents will differ in phase 
from one another by 60°. If we had a separate outgoingand 
return wire for each of the three circuits we should need no 
fewer than 6 lines from the machine to the (3-phase) motor 
which it supplied. But as will be seen, by adopting proper 



Fig. £3.— Three-phase Currents differing 60° in Phase. 


methods of grouping, this complication is unnecessary, the 
number of lines being capable of being reduced to four or to 
three. If an earth return were admissible, the number of 
actual line wires might even be reduced to two. 

Before we pass to the consideration of any modern poly¬ 
phase generators we must devote a little attention to the 
effect of breadth of the windings in the coils of the armature. 
Consider a multipolar revolving field-magnet such as Fig. 24, 
in which we will assume that the pole-pieces have been so 
shaped that the magnetic field in the gap-space between 
poles and armature cores is distributed in a manner so as 
to give a regular and smooth wave-form for the curve of 
electromotive force induced in any conductor placed in the 






Polyphase Generators . 


23 


gap. We will represent electromotive forces which act 
upwards, or towards the reader, by a dot, and those which 
act downwards, or from the reader, by a cross placed in 
the section of the conductor. Then, as in Fig. 25, there will 
be induced electromotive forces acting upwards in those con¬ 
ductors in front of which the south pole is moving to the 




Fig. 25. 


right, and downwards in those which the north pole is passing. 
But these electromotive forces will not be equal at the same 
instant amongst themselves: they will be greatest in those 
conductors which are most active—that is to say, in those 
which are passing through the strongest magnetic field. Each 
conductor will go through an equal cycle of inductive action, 
but it is clear that they come to their maximum one after the 


Fig. 28. 




Fig. 27. 


other. For convenience we will suppose this maximum to 
occur in each conductor as the middle of the pole passes it. 
Now suppose (as is usual in construction) that a number of 
these conductors are connected up, as in Fig. 26, to form a 
coil; their electromotive forces will be added together. If a 
view is taken, as in Fig. 26, where we are supposed to 































24 


Polyphase Electric Currents. 


be looking back at the poles passing from right to left, we 
shall understand this a little more plainly. A moment later 
the north pole will come right behind the coil as in Fig. 27. 
This figure shows that there can be no advantage in having 
the inner windings of the coil much nearer together than the 
breadth of the pole-face, since at this instant their electro¬ 
motive-forces are opposing one another. There is some 
advantage in filling up the coil a little narrower than the actual 
pole-face because of the disposition of the magnetic field. 
But the actual electromotive-force generated by a coil of a 
given number of turns would be greater if they could be all 
of the same size, so that all should reach their maximum 
action at the same instant. 

This point may be further elucidated by the use of a 


clock-diagram. Suppose 



c' 


the maximum electromotive-foix e 
generated in one conductor to be re¬ 
presented by the pointer O A in Fig. 
28. Then the projection of O A 
upon the vertical line O P gives the 
value of the electromotive-force at 
the instant when the angle A O P 
corresponds to the phase of the in¬ 
duction that is going on in the 
period. Let there be two other con¬ 
ductors situated a little further 


along, so that their electromotive- 
forces would be represented separately by O B and O C. We 
have to find what the effect- will be of joining them all in 
series. By the rules for compounding vector qualities, we 
shall find their resultant by drawing from A the line A B' 
equal and parallel to O B, and from B' the line B' C' equal 
and parallel to O C. Then O C' is the resultant; and its 
projection O Q upon the vertical line gives the instantaneous 
value of the united electromotive-force of the three conduc¬ 
tors. Had they all been placed close up to one another at A 
without any difference of phase between them, the resultant 
would have been O A'", and this projected upon the vertical 
line gives O P'" as the instantaneous value. 







Polyphase Generators . 


25 


A numerical way of considering the matter maybe useful. 
Suppose each conductor to generate an electromotive-force, 
the virtual value of which is 1 volt: then if three such con¬ 
ductors are connected up in series their total electromotive- 
force cannot be 3 volts unless they lie so close together that 
they all receive their maximum values at the same time. Any 
spreading out of the coils must lower the value of the resultant 
electromotive-force. 

It is therefore worth while to calculate a breadth coeffi¬ 
cient for a coil of any particular angular breadth. Let the 
symbol V* stand for the difference of phase between the centre 
of any coil and its outermost conductor on either side. If the 
machine has a two-pole magnet the value of is simply half 
the angular breadth (in radians) subtended by the coil. If the 
machine is multipolar, having p pairs of poles, then the angle 
V' of the phase difference will be equal to half the angular 
breadth (as measured on the machine) multiplied by p. Or, 
if the linear breadth of the coil measured along the circum¬ 
ference be called 5, and the diameter of the machine is 
d , the angle f of the phase difference corresponding to the 
half-breadth will be = b p -f- d. Now the average value of 
the virtual electromotive-force in all the conductors comprised 
within this breadth will be given by the formula 

1 /V .7 

— / e . cos y . d y ; 

J 0 

where e is the virtual value electromotive-force in any one 
conductor and y is the angle of difference of phase between 
the E.M.F. in any conductor of the coil and the E.M.F. in the 
central conductor of the coil. If we call the part of this 
expression which depends on 0 the breadth coefficient, and 
denote it by q, then performing the integration we have 
q == sin -f- V*. 

In order to give some numerical values we may anticipate 
some of the constructions later shown. For instance, in a ring 
wound with four coils each covering one quadrant (as in some 
2-phase motors, see Fig. 49), 

4> = 45° = 0-785 radians; q = 0-90. 


26 


Polyphase Electric Currents . 


In the case of a ring’ wound with three coils, each covering 
120° (see Fig. 54), 

V» = 60° = 1-05 radians; q — 0-82. 

In the case of a ring wound with six coils each covering 60° 
(as in Fig. 5T), 

= 30° = 0-523 radians; q — 0*95. 

As an example, consider a multipolar two-phase generator, 
having armature conductors carried through holes in the core 
disks, and having 12 equally spaced holes in the repeat 
from one N-pole to the next N-pole. In this case six of 
the conductors belong to one phase, six to the other, and 
each group will consist of three up and three down. The 
three in a group occupy one-fourth the whole breadth, or are 
equivalent to 90° on the circle of reference: but as the con¬ 
ductors are confined within holes, the virtual angular distance 
between the two outer conductors of the three is 60°, and the 
half-distance 30°; whence q — 0-95. 

Before leaving this question of the compounding of two 
electromotive-forces that are in different phases with one 
another we may note that the principle 
of vector summation used above leads 
to a very simple result where two 
electromotive-forces are concerned. 
Let O P represent one of these electro¬ 
motive-forces, O Q the other, the an¬ 
gular phase difference between them 
being P OQ or 0. Compounding 
them in the usual way, by drawing 
P R equal and parallel to O Q we get 
the resultant O R, which represents 
the magnitude and relative phase of 
the resultant electromotive-force. Here by ordinary geometry 

O R=|/OP 2 +OQ 2 + 20 P'O Q cos 0. This is obviously a 
maximum when the phase-difference is zero. 



i .m. X). 


1 Compare Thomson and Tait’s Treatise on Natural Philosophy,\ ol. i. § 58. 






Polyphase Generators . 


27 


MODERN POLYPHASE ALTERNATORS. 

We are now prepared to examine some modern examples 
of polyphase machines. 

First the three-phase generators at Lauffen. These are 
driven by turbines in the river Neckar, and were erected in 
1891 for supplying current to the town of Heilbronn, six miles 
distant, They were, however, at first employed in the now 
famous historical transmission of power from Lauffen to 
Frankfort, a distance of 110 miles, on the occasion of the 
Frankfort Exhibition. They were constructed by the Oerli- 
kon Co. of Zurich from the designs of Mr. C. E. L. Brown ; 
and have revolving internal field-magnets with an external 
armature with zigzag arrangements of conductors passing 
through holes in the core-rings. Fig. 30 gives a general view, 
whilst Fig. 31 shows the field-magnet after the armature has 
been slid away for inspection. The machine generates three 
currents, each of 1400 amperes, at a pressure of about 50 volts; 
taking 300 horse-power when running at 150 revolutions per 
minute. The armature has an external diameter of 189*4 cm. 
(nearly 6 feet) and an internal diameter of 176*4. The 
total thickness of core-rings, parallel to the shaft, is 38*0 cm. 
Around the inner periphery of the core-rings are 96 circular 
holes 33 mm. in diameter, at distances of 60 mm. apart. Each 
of these holes is lined with a tube of asbestos, and through 
each passes a solid copper rod 29 mm. in diameter. The 
core-rings, built up of segmental stampings, are assembled in 
a strong cast-iron frame. The winding, if such it can be 
called, is in three independent zigzags of 32 conductors each 
connected according to the following scheme :— 


Set A, 1, 4, 7, 10. 91, 94. 

Set B, 95, 92, 89, 86,. 5, 2. 

Set C, 93, 90, 87, . 3, 96. 


The ends of Nos. 94, 2, 96, are connected to a common 
junction J, while Nos. 1, 95, and 93 are severally brought out 
to three external terminals. This constitutes a star-winding 



















































Polyphase Generators. 


29 


(p. 43) ; the connections of the circuits are shown in Fig. 32, 
the general arrangements of the windings being illustrated in 
Fig. 33. 

The gap-space between the armature core-ring and the 
pole-faces of the field-magnet is 6 mm. This field-magnet 
has 32 poles. It is of great solidity and simplicity, having 
but a single magnetic circuit. The exciting coil is wound in 



Fig. 31.— Field-magnet of Three-phase Alternator at Lauffen. 

a channel on the periphery of a sort of pulley of cast iron, 
to which are bolted two steel rims, each carrying 16 polar 
expansions or horns. Each of the polar faces has an area of 
36 X 16 sq. cm. The channel is 18 cm. wide and 9 cm. deep. 
In it lie 496 windings of copper wire 5 mm. diameter. A 
section of this channel is given in Fig. 34; and Fig. 35 
illustrates the way in which the polar horns project inwardly, 
the N-poles between the S-poles over the exciting coil. This 

































3 ° 


Polyphase Electric Currents . 




Fig. 38.—Arrangement of Windings of Three-phase Alternator. 



















Polyphase Generators. 


3 i 


arrangement reduces the cost of construction and of excitation 
to a minimum. In fact, on open circuit only 100 watts are 
spent on excitation—one-twentieth of one per cent, of the out¬ 
put ; and at full load, when the armature reaction is a maxi¬ 
mum, it is still far less than one per cent. This excitation is 
furnished by a small separate dynamo. The exciting current 
is conveyed to the rotating part by means of flexible metallic 
cords running over insulated pulleys, in lieu of the usual 
contact-rings and brushes. At full speed and normal voltage, 
the loss by friction and hysteresis is 3600 watts, or under 



MAGNET 

1*7 per cent, of the maximum output. The loss of resist¬ 
ance of armature windings at full load is 3500 watts, making 
total loss about 4 per cent., and commercial efficiency over 95 
per cent. The heating is, in the total absence of eddy-currents, 
quite negligible. The weight is 4^ tons. As there aie sixteen 
pole-pairs, and the speed is 150 per minute, the frequency is 
40 periods per second. The electromotive-force generated 
in each of the three windings, as measured between the 
common junction J and the outer terminal, could be increased 
up to 55 volts. 





























































32 


Polyphase Electric Currents. 


The following are some of the measurements made on this 
machine by the official jury under Prof. H. F. Weber in 
1891:— 


Horse¬ 
power 
of Turbine. 

Electrical 
horse-power 
yielded by 
Alternator. 

Horse¬ 

power 

lost. 

Effi¬ 

ciency. 

Current 
in one 
circuit. 

Volts 
between 
common 
junction and 
terminals. 

Speed. 
Revolutions 
per minute. 

87*4 

75-1 

12-3 

per cent. 
88 

336 

54-7 

150 

120-1 

107-5 

12-6 

90 

470 

56 1 

150 

154-7 

142-2 

12-5 

92 

644 

54-2 

149-7 

167-2 

154-4 

12-8 

92-6 

677 

1 

55-9 

149-5 


The tests were not carried up to full load, but the jury 
remarked that, assuming the losses to increase in the same 
proportionality as indicated by the above figures, the effi¬ 
ciency at the full load of 800 horse-power would be 95*4 
per cent. 

The method of construction adopted in the armature of 
this machine is worthy of note. To Mr. C. E. L. Brown 
belongs the credit of introducing the practice of embedding the 



conductors in holes pierced through the core disks. In nearly 
all polyphase machines, whether generators or motors, one 
finds, in fact, the conductors either threaded thus through holes 
or else imbedded in slots between deeply cut teeth. Toothed 
cores, as in Fig. 36, are now almost universal in American 
dynamos and motors ; but the pierced cores are distinctively 
Swiss. At the Oerlikon works circular holes are largely used. 
Messrs. Brown, Boveri & Co., of Baden (Canton Aargau)* 
sometimes employ circular perforations, but their standard 
style is, as in Fig 37, an oblong hole about 50 mm. long and 















Polyphase Generators . 33 

20 mm. wide, the insulating lining being a strong tube of 
corresponding section made of a preparation of paper. 

There are several advantages accruing from the bedding 
of the conductors in iron. The mechanical construction is 
improved, for the conductors are securely held and driven 
without the need of any binding wire. Centrifugal force does 
not displace them, and the clearance between the revolving 
and the stationary parts may be greatly reduced, thereby 
economizing exciting power. But more important than these 



Fig. 38. —Polyphase Generator of the Oerlikon Co. 
are two other advantages. There are no useless eddy-currents 
generated in conductors so bedded in iron, so they need not 
be laminated or stranded, but may be made of solid copper 
rods. Also there is no tangential drag of the magnetic field 
upon conductors so bedded : the drag comes on the iron 
instead of coming upon the copper. 

A more recent (1894) 3-phase generator, built by the 
Oerlikon Company, having the same general features of field- 
magnet and of armature, but with various improvements in 
detail, is described and depicted in the third (1894) edition of 
3 




34 Polyphase Electric Currents. 

Kapp’s ‘Electric Transmission of Power.’ A general view 

is shown in Fig. 38. , t 

Asa second example of a polyphase generator we select 
the large 1000 horse-power machines shown at the Chicago 



FlU. 39.—WESTINGHOUSE TWO-PHASE GENERATOR. 

Exhibition by the Westinghouse Co. of Pittsburgh. One of 
these is shown in Fig. 89, which should be compared with 
Fig. 2. It is virtually a double machine, having side by side 
two similar field-magnets, and within two similar armatures 
upon the same shaft. But the armatures are “ staggered ” ; 
that is to say, they are so mounted that one of them has an 
angular advance over the other equal to one-half the angular 
breadth from a N-pole to a S-pole. By merely shifting 
the second armature the same machine might be used as 
one single-phase alternator. In this case the adoption of a 





Polyphase Generators. 


35 


2 -phase system is not accompanied by any economy of space 
or material in the machine. These alternators are of 750 kilo¬ 
watt output, running at 200 revolutions a minute, and having 
a frequency of 60 periods per second. The lield-magnets each 
consist of 36 poles of laminated mild steel cast solidly into 
the outer yoke. Each armature has 36 teeth; and between 
these are slipped in and secured the previously-wound 
armature coils. 

Some years ago Mr. William Stanley, of Pittsfield (Mass ), 
introduced a 2-phase alternator of the “inductor type,” in 
which the whole of the copper windings, both primary and 
secondary, are fixed, the only moving part being of iron. 

The Brush Electrical Engineering Company, of London, 
has produced 2-phase alternators on Mr. Mordey’s well-known 
type of construction by the following modification of the 
armature. In order to allow half the coils to be displaced 
through the breadth of half a coil, two coils are removed at 
opposite ends of a diameter. A similar modification makes 
the machine applicable for 3-phase work. Mr. G. Kapp’s 
recent alternators are capable of being similarly adapted. 

In recent years various. forms of polyphase alternators 
have been introduced by Messrs. Brown, Boveri & Co., of 
Baden, Switzerland, the designs being worked out by Mr. 
C. E. L. Brown, formerly of the Oerlikon Company. 

Some of these machines present no special feature to 
distinguish them from ordinary alternators beyond having 
the coils of the armature arranged in sets of twos or threes 
to correspond to 2-phase or 3-phase work. 

Recently Mr. Brown has adopted a form of revolving 
field-magnet having a series of outward-pointing radial poles, 
with the peculiarity that only alternate poles are wound with 
exciting coils, the intermediate ones being simply projections 
of cast iron of larger cross section than the intermediate 
cylindrical cores that receive the coils. 

Another feature introduced by Brown in the winding of 
alternators, whether for single-phase, 2-phase or 3-phase 
work, and applicable to motors as well as generators, is the 
arrangement of the connecting wires where they emerge out¬ 
side the core-rings in two sets in different planes. This con- 


36 


Polyphase Electric Currents . 


struction may be noticed in Fig. 171 and Plate II. Though a 
detail it is of great use in obviating risks of short-circuit. In 
Fig. 40 this construction is diagrammatically displayed, show¬ 
ing how both the A set and B set of windings in a 2-phase 
generator may he grouped so as to utilize for each lap two 
sets of holes side by side. This has some advantages over 
using single holes of very large size. These would interfere 



more with the magnetic circuit, and tend to set up greater 
heating in the polar parts of the field-magnet. Single holes, 
being of greater depth radially, would, moreover, cause greater 
magnetic leakage. 

1 ig. 41 shows an adaptation of the method of arranging 
the windings of a 8-phase generator, so that the loops of 
coil can still be situated in two planes. The A coils will of 













Polyphase Generators. 


37 


course be connected together in series, though they lie 
alternately in the inner and in the outer positions; and so 
likewise the B and the C coils (see Plate II.). 

Fig. 42 shows how the core-rings may be utilized for a 
3-phase generator (or motor) with a winding in which all 
the holes are not employed. This winding was used to save 
the necessity of making a fresh set of stamps for the core¬ 
disks. The magnetic reactions are less, when the unused 
holes are left in the spaces as shown, than would be the case 
if the core-rings at these parts were not pierced. 

To Mr. Brown is due the introduction of the vertical-shaft 
type of generator so admirably adapted for running direct 
from a turbine. A large number of these machines are now 



Fig. 43.—Brown’s “Umbrella” Type of Alternator. 


in operation. One of these machines, a 3-phase generator, 
has for some years done excellent work at Schonenwert near 
Aarau in Switzerland, furnishing current for motors in a large 
shoe-factory. More recently the town of Aarau has been 
provided with a central station which derives its power from 
the waters of the river Aar by means of turbines. 

A general view of this “ umbrella ” type of generator is 
given in Fig. 43. Its moving part—in this example the field- 
magnet with a large number of radial poles projecting out¬ 
wards—revolves upon the shaft being hung upon a six-armed 
spider. Outside it is the stationary armature of pierced core¬ 
rings, having the windings coupled up by angular end con¬ 
nections. The Oerlikon Company has also constructed large 



























































39 


Polyphase Generators . 

alternators of the umbrella type, for the power stations at 
Bellegarde, Bremgarten, and at Hochfelden. Fig. 44 gives a 
view of the latter station, showing the three generators, which 
were designed by Mr. O. E. L. Brown in 1890. They are 
8-phase machines, each of 200 horse-power, running at 180 
revolutions per minute. Excepting in having the vertical 
shafts directly above the turbines by which they are driven, 
they closely resemble the Lauffen generators. They give 86 
volts pressure between the terminals. To raise the voltage 
each is connected to a 8-phase transformer immersed in oil; 
one of these transformers being visible on the right hand of 
the cut. The pressure is raised to 18,000 volts, at which 
pressure the currents are conveyed by three wires, each 4 
millimetres in diameter, to the Oerlikon Works (a distance of 
24 kilometres, or about 15^ milles), where by means of step- 
down transformers of similar construction the pressure is 
lowered to 190 volts, and the currents are distributed for 
lighting and power at this pressure. 

The Niagara Alternators .—When the project of utilizing 
the water-power of Niagara by turbines was taking shape the 
Cataract Construction Company invited many different manu¬ 
facturers in Europe and in America to submit plans. The 
machines were to be of 5000 horse-power, driven by turbines 
making 250 revolutions per minute. Many of these designs 
were extremely good; nevertheless it was determined to have 
the machines manufactured in America, owing to the high 
tariff charged on imported goods, and to the cost of trans¬ 
sport. Some of the designs (including those of Mr. Brown) 
were of the “umbrella ” type, but for various reasons (turn¬ 
ing mainly upon the constructive difficulties arising from 
size and speed) Professor Forbes and Mr. Coleman Sellers 
were instructed in May 1898 to get out further plans for al¬ 
ternators of the proposed type. Professor Forbes fixed upon 
an externally-revolving umbrella field-magnet, with inward¬ 
ly-pointing poles held together by an external annulus of 
steel, as possessing both great strength and a large fly-wheel 
action. At first he prepared designs for a 2-phase machine, 
having the low frequency of 16f periods per second, with 8 
poles. Eventually, after the Westinghouse Company had 


40 


Polyphase Electric Currents . 


been selected as manufacturers, it was decided to fix the fre¬ 
quency at 25, and to wind the armatures for 2000 volts. The 
drawings published by Professor Forbes 1 relate to the earlier 
design, and have certain complications about the armature 
which became unnecessary when it was decided to keep the 
voltage at 2000, instead of working at 30,000 volts. 



Fig. 45 gives a sectional drawing 2 of the Niagara machine 
as built. Its outer rotating field-magnet consists of a wrouglit- 
steel ring, to which are bolted internally twelve inward 
pointing cast-iron pole-cores. It is hung to the vertical shaft 
by a six-arm cast-steel spider. The shaft passes up through 
a bronze bearing, which is supported by four arms projecting 
i nwardly from a cast-iron ring. The latter is itself adjustably 
fixed within an outer cylindrical mantle of cast-iron, which 
stands on the foundation ring and carries the stationary in- 

1 Journal of the Institution of Electrical Engineers , November 1893. 

2 From the Electrical Engineer (N.Y.) of January 16, 1895. 

























































































Polyphase Generators . 


4i 


temal armature. The core of this is built up of thin sheet 
iron segmented disks, clamped together by eight bolts of 
nickel-steel. There are 187 nicks or grooves in the outer face 
of the core to receive the copper conductors. These are 874 
in number, rectangular, being 32 X 8 millimetres in section, 



Fig. 46.—One of the Niagara Generators. 
two such bars lying side by side in each groove between the 
armature teeth. The insulation is of mica. They are coupled 
up by bent end connectors in two independent circuits. The 
actual voltage at the speed of 250 revolutions per minute is 
2250, the output in each of the two circuits being 775 am¬ 
peres. As there are twelve poles the frequency at this speed 
is 25 periods per second. The field-magnet windings are 














42 


Polyphase Electric Currents. 

supplied with continuous current (derived from a rotating 
transformer) through two slip-rings fixed on the top of the 
shaft. Fig. 46 gives an external view of one of the machines. 
The total height is about 13 feet. 

The Strassburg G-enerators .—The 3-phase generators re¬ 
cently constructed by the Allgemeine Company, of Berlin, 
for the City of Strassburg are of the “ inductor ” type with¬ 
out any moving copper. 

Asynchronous Generators .—It has been found by several 
experimenters independently—amongst them Mr. C. E. L. 
Brown, and the Engineers of the General Electric Company, 
at Schenectady, New-York—that the asynchronous motors, 
whether polyphase or monophase, can act as generators pro¬ 
vided they are mechanically driven at a slightly higher speed 
than that of synchronism (see p. 145). But it is not possible 
to work a circuit with only one such machine to be used as a 
generator—it is not self-exciting. There must be an alternate 
or polyphase current already supplied to the mains or ter¬ 
minals. It would probably be convenient in those central 
stations where the load is apt to show very sudden increase, 
to use one or more asynchronous generators along with other 
alternators, as the asynchronous generator might be kept 
turning as a non-loaded motor at a speed just below syn¬ 
chronism until required. On merely quickening up the speed 
of its engine (without waiting to “ synchronize ”) it will 
begin to work as a generator, its electromotive impulses syn¬ 
chronizing perfectly with those of the circuit, though its 
speed is not synchronous. 

In some experiments made in Sweden 1 by Mr. Danielson 
in 1892 a 3-phase asynchronous motor was coupled with a 
synchronous 3-phase generator. The former was then driven 
as generator, and the latter used as motor, running on a 
brake. It was found that the asynchronous machine would 
not generate if the circuit included only resistances (lamps) 
or resistance with self-induction. 


1 Electrical World (N.Y.), Jan. 1893, p. 44; Electrical Review , xxxii. 
p. 169, Feb. 1893. 


Combinations of Polyphase Currents . 43 


CHAPTER IT. 

COMBINATIONS OF POLYPHASE CURRENTS. 

Not until after the growth of the idea of combining currents 
in different phases for driving motors did any one suggest 
ways of combining into regular systems the separate groups of 
coils in which induction was occurring in different phases. 
The combining of currents of two or three phases has been 
usually considered in relation to motors; it may, however, be 
equally usefully discussed in relation to generators. 

There are two general ways of combining polyphase 
circuits, which may be characterized respectively as star- 
groupings and mesh-groupings. In the star-grouping, the coils 




in which the power is generated or absorbed are joined to a 
common junction from which they branch star-wise each to its 
own line. The comparison may be made in the concrete case 
of a 3-phase system. Fig. 47 is a diagram of a star¬ 
grouping of three coils, a, b and £, designed to receive currents 
in regular rotatory order, the current flowing in toward the 
centre first through a (and passing out by one or both of the 
other coils), then through b, then through c . Fig. 48 shows 
three coils, q and r, grouped in mesh fashion. Here the 


44 


Polyphase Electric Currents. 


coils form a closed mesh connected to the circuit at the 
corners. 

There are also several more complex groupings in which 
both these features are used at the same time. Fig. 60, on 
p. 48, shows a combination of the two systems. 

A further illustration is afforded by a simple 2-phase 


system, in which the several 
separately considered. 



Fig. 49. 


possible groupings may be 



Fig. 50. 




Fig. 51. Fig. 52. 


(1) Independent windings. The coils on the generator 
which are in the same phase may be connected together in 
any methods used in single-phase machines, and the coils 
belonging to the other phase may be likewise so connected ; 
so that we have two totally independent circuits as shown in 
Fig. 49, wherein the coils a and c belong to one circuit, con¬ 
nected to the lines m and o, and the coils b and d constitute 
an entirely separate circuit joined to the lines n and p. 

(2) Star-grouping. The coils or groups of coils may each 


















45 


Combinations of Polyphase Currents . 

have one terminal joined to a common junction J forming a 
star and the free terminals joined to the line-wires, as shown 
in Figs. 50 and 51. In Fig. 50 the coils are represented as 
wound upon a ring; whereas in 
Fig. 51 they are wound upon polar 
projections. They differ in their 
magnetic relations ; but, considered 
simply as circuits, they are identi¬ 
cal. 

(3) Mesh-grouping. The coils 

may be connected together so as 
to form a closed circuit and the 
line-wire attached to the points 
of junction between the coils, as Fro* 53 * 

shown in Fig. 52, which is an ordi¬ 
nary 4-part Gramme ring, having, however, its connections 
joined to four lines instead of being provided with a 4-part 
commutator. 

(4) In case No. (1) where the coils are otherwise 
independent, two of the terminals belonging to different 
phases may be connected together and a single return-wire 
employed as shown in Fig. 53, instead of having four line- 
wires. 



COMBINATION OF ELECTROMOTIVE-FORCES. 

It is necessary to consider in each of these cases how the 
electromotive-forces of the separate coils are combined, and 
the effect of such combinations upon the electromotive-forces 
between the line-wires. Let us say that the E.M.F. of the 
coil a follows the law v sin 6 where v is the maximum value 
attained in each period, as calculated from previous con¬ 
siderations (see pp. 8 and 25). 

Two-phase Systems. —If the coils are joined up inde¬ 
pendently, as in Fig. 49, or in a star-grouping, as in Fig. 50, 
the E.M.F. between the terminals m and o will be 2 v sin 6. 
In the case of the star winding there is also a pressure of 
\T2 v sin (6 + 45°) between the terminals of m and n ; that 







46 


Polyphase Electric Currents . 


is to say, the pressure between the two line-wires of different 
phases is 1-4 times the pressure at the terminals of one coil 
and is 45° of phase in advance of the foremost coil. 

When the coils are joined up in a mesh, as in Fig. 52, the 
E.M.F. between m and p is of course the E.M.F. generated 
in a , namely v sin 0, while the pressure between n and p fol¬ 
lows the law V 2 v sin (0— 45°) ; that is to say, it is 1*4 
times the pressure at the terminals of one coil and is midway 
in phase between coils a and b. 

Where a common return is used the E.M.F. between each 
outgoing wire and the return will be simply double the 
E.M.F. of one coil, but the E.M.F. between the two out¬ 
going wires will be 1-4 times this or 2 4/^2 v sin (0 + 45°). 

Three-phase Systems .—In order to find how the pressure 
varies between the line-wires of a 3-phase system when the 
coils of the generator are joined up in star fashion, let us 




consider Fig. 54. Coil «, as before, may be taken as a 
standard of reference, the pressure at its terminal being v sin 0 . 
Consider the E.M.F. outward from the common junction as 
positive. The E.M.F. in b is v sin (0— 120°). 

The pressure between m and n is the differences of the 
electromotive-forces in a and 5, or v sin 0 — v sin (0 —120°) 
== 4/^3 v sin (0 + 30°). 

Example: If v = 141, the virtual volts generated by 
a are 100. The pressure between the lines m and n 







Combinations of Polyphase Currents. 47 

= V~S X 100 = 173 virtual volts. The phase of this 
pressure is 30° in advance of phase of a. 

The clock diagram given in Fig. 55 shows the matter 
clearly. The lines a, b and c represent the E.M.F. in the 
respective coils. To subtract £>, produce it backwards as 
shown — 5, and then completing the parallelogram we get 
the resultant E.M.F. 30° in advance of a , and fg times 
as great. 

If the coils of a 3-phase system are joined up in mesh 
fashion, as shown in Fig. 56, the E.M.F. between 0 and m is 
simply the E.M.F. generated in a. 




A 3-phase generator or motor is not generally built with 
the simple arrangement of three coils as shown in Fig. 54. 
There may be six coils or sets of coils, as in Fig. 57, in which 
case those pairs which are opposite to each other in phase are 
joined in series, so as to act like one coil of double the E.M.F. 

Fig 57 is in fact a diagrammatic representation of the 
arrangement of coils in Fig. 22, only the coils are spaced 
round an entire circle instead of merely spanning the space 
between one N-pole and the next. The coils being joined in 
pairs, we have virtually only three coils. Taking them in 
the order 

a + d 

c+f 

e + b 

we see that the pairs are 120° apart, and can be treated in 
the same way as the three coils in Fig. 54, that is to say, we 





48 


Polyphase Electric Currents . 

may join them up star fashion, as in Fig. 58, in which case 
the E.M.F. between m and o will be 2 vsin (e + 80°), or 
they may be joined up in mesh fashion, as in Fig. 59, in 
which case the E.M.F. between k and s will be 2 v sin 0. 




. A combination of the star and mesh groupings is shown 
diagrammatically in Fig. 60. Fig. 61 shows how six coils 
wound right-handedly on a ring might be so connected. In 
this case the E.M.F. between any two terminals, for example 
A and B, would follow the law 2 v sin (0 — 60°) where the 
E.M.F. in a is v sin 0. 




Such combinations were first suggested by Dobrowolsky 
with the object of gaining in a motor a more uniform torque 
at different points of the revolution than would be attained 
by a set of coils in three phases only. 











Combinations of Polyphase Currents . 


49 


COMBINATIONS OF CURRENTS. 


It is necessary also to consider the relative values of the 
current in the different conductors of a polyphase system 
when they are joined up in star or in mesh. In the first place 
there are a few general rules which are of service in deter¬ 
mining these values in any given arrangement. 

1. Where any number of wires meet at a common junction 
the algebraical sum of the instantaneous values of all the 
currents (taking, say, the direction outward from the junc¬ 
tion as positive) is equal to zero. 

2. In the case of alternating currents this rule is only 
applicable to instantaneous values and not to the effective 
values of the currents, unless they are all in the same phase. 

3. Where two currents differing in phase meet in a 
common conductor, their resultant can be found by the 
graphic method given in Fig. 29, where O P and O Q may 
represent the two currents and O R their resultant. Or the 
following formula, which follows at once from the graphic 
construction, may be employed :—If a sin (6 + is one of 
the currents and b sin (0 + ^ yy ) is the other, then their sum 
is 4 / a 2 + b 2 -b 2 a b cos (j> u — ^ y ) sin (0 + ^ yyy ) 

where 


tan f m 


a sin 0 y H- b sin ^ yy 
a cos <j>j + b cos (t> n 


4. It is necessary to adhere strictly to some notation 
indicating the directions taken as positive and negative. For 
instance, in considering a star-grouping of coils in a gen- 
arator, it is convenient to take the direction outward from the 
common junction as positive, and in the line-wires the positive 
direction will then be from the generator to the lamps or 
motors. In a mesh-grouping the direction clockwise round 
the mesh may be taken as positive. 

In applying these rules to determine the relative values 
and phases of current in any system, we first of all observe 
that the currents will be dependent upon the impedances of 
4 




50 


Polyphase Electric Currents. 

the various circuits. We can only lay down general rules 
where we have a symmetrical system symmetrically loaded. 

Taking then a 2-phase generator with mesh-grouped coils 
whose two circuits are equally loaded, the current in the line 
m (Fig. 52) is the sum at every instant of currents in the 
coils a and b. If the current in a — C sin 0, and that in 
b = C sin (0 — 90°), the positive direction of the current 
in b being away from the junction, we must write 

C sin 6 — C sin ( 0 — 90°), 

from which we get the current in m — |/ 2 C sin (0 + 45°). 

In the case of star and independent windings, the currents 
in the coils are necessarily the same as in the line-wires. 

When in a 2-phase system, one return-wire is used as in 
Fig. 49, even though the load on each phase may be the same 
the difference of phase between the two currents is increased 
to a little more than 90°, that is to say, the current in the 
leading phase rises to a maximum a little earlier than it 
would if the currents were independent, and the other 
current rises to a maximum a little later; but this departure 
from 90° difference of phase may be made as little as we like 
by decreasing the resistance of the line. Even in a line 
wasting 15 per cent, of the total power, the difference in phase 
is oidy increased by about 6 0 , 1 so that for practical purposes 
we may combine the currents as in the case given above for 
the mesh winding, and say that the current in the return- 
wire is |/ 2 or 1-4 times as great as in the other wires and 
midway between them in phase. 

The currents in the coils of a 3-phase generator grouped 
in a mesh can be combined in the same manner as in the case 
of two phases. 

We have from Fig. 55, p. 46, 

sill 0 -sin ( 0 - 120 °) = /8 sin (Q + 30°). 

That is to say, that the line-wire current is 4/3 01 . 1-73 times 
as great as the current in the coils. Comparing these results 
with those obtained for the electromotive-forces we see that 


1 Rodet et Busquet, Les Courants Polyphases, p. 10. 


5i 


Combinations of Polyphase Currents . 

in star grouping the electromotive-force between the line- 
wires is greater than at the terminals of the coils, and the 
current remains the same, while with the mesh-grouping, the 
current in the line-wire is greater than in the coils, but the 
electromotive-force remains the same. 


GROUPING OF LAMPS IN A POLYPHASE SYSTEM. 

The foregoing ideas may be illustrated by the various 
wa) r s of grouping lamps in polyphase circuits. 

Lamps on Two-phase Circuit .—Suppose a generator G, 
Fig. 62, supplies two currents in quadrature. These may be 
used, as in this figure, as two independent services to supply 
lamps, while for motor purposes all four wires can be brought 


IMF! 

\ HIT 



T.'a, M 



into operation. But, as has been already pointed out, three 
wires only need be used, a middle wire w, Fig. 63, serving as 
a common return. For carrying equal numbers of lamps 
on the two circuits the middle wire must be thicker than the 
two outer wires, but need not be of double section as the 
currents are out of phase ; the maximum current in the 


middle wire being |/2 times as great as that in the other 
wires. The voltage across from a to b will not be double 
of the voltage from a to m or from J tow; but will be 
V2 times as great. In fact, if the lamps in the two rows were 
TO-volt lamps, a third row might be added of 100-volt lamps 
connected from a to b. 

A mesh system of lamps may be arranged as in Fig. 64, 
using four line-wires. In this case if the lamps were 100-volt 
lamps, the voltage from a to a'would be 141-4 volts, and that 


















52 


Polyphase Electric Currents . 

from b to b r also 141*4 volts. With equal numbers of lamps 
the current in any one of the four lines will be 1*41 times 
that required for any one row of lamps. 

If the lamps are arranged in a star system of grouping, as 
in Fig. 65, there will be some advantage in connecting the 
common junction J to earth (i. e. to a common return, which 
need not be insulated), provided the coils of the generator 
are also grouped starwise, so that they can also be earthed. 
This is really equivalent to a 4-phase system having the 
phases in two coincident pairs. If the lamps are 100-volt 
lamps there must be 200 volts from a to a r or b to V ; and 
there will be 141*4 volts from a or a! to b or V. 




Lamps on Three-phase Circuit. —Three-phase circuits akin 
to the two last-mentioned, are illustrated in Figs. 66 and 67. 
Fig. 66 represents a mesh-grouping. With equal numbers of 
lamps in the three rows, the current in any one of the three 
lines will be equal to 1*73 times that required for any one 
row of lamps. 

If the lamps are grouped star-wise (Fig. 67), the mid-point 
may be earthed, provided the corresponding point on the 
generator (or transformer) is also earthed. This was done in 
the case of the lamps at Frankfort on the 3-phase transmission 
from Lauffen in 1891, and is carried out in the 3-phase 
distribution at Heilbronn (p. 217). If the lamps are 100-volt 
lamps, the pressure between any two of the three circuits will 
be 173 volts. Neither the star nor the mesh-grouping of 
itself secures absolute independence of the various parallels 
of lamps, though the star methods are, on the whole, more 

























Combinations of Polyphase Currents . 53 

nearly so. When lamps are turned on or off in any one row 
the pressure of the other rows is always more or less affected 
thereby; but the use of the common return from the centre 
of the star system greatly reduces this. 

Amongst the curiosities of polyphase work may be men¬ 
tioned incandescent lamps with three wicks meeting in a point, 




and three outer terminals. Such were first shown in 1891 by 
Dobrowolsky. Others having three spirals were constructed 
by the Edison-Swan Company for the author for his lecture 
at the Royal Institution in February 1894. At the same 
lecture a 3-phase arc-light was shown with three carbons 
meeting at 120° to one another. The arc or flame showed a 
gyratory movement. 

ECONOMY OF COPPER. 

It has been claimed that by the adoption of polyphase 
systems, as compared with single-phase systems, there is 
effected a saving in the total weight of copper needed for 
the transmission of a given amount of power to a given 
distance. Of the correctness of this view in the main there 
can be no question; the conflict of opinion which has arisen 
being due to the circumstance that the various disputants 
have taken different criteria as the basis of comparison. The 
economy in copper—which is the most important factor in 
the cost of long-distance transmission—depends, as every 
electrical engineer knows, upon the electric pressure at which 
the current is transmitted; so that, in comparing together 
different systems, the comparison, to be fair, should be made 


















54 


Polyphase Electric Currents . 

upon the basis of employing equal voltage. But the ques¬ 
tion arises, Between what points is the voltage of the system 
to be taken in the comparison? 

But it must be remembered that while high voltage is the 
secret of economy of copper in electric transmission and dis¬ 
tribution, the voltage at which a system can be operated is 
determined by different considerations in different cases. In 
low-pressure systems of distribution the voltage is determined 
by the glow-lamps ; and as these are not practicable for 
voltages over 100 to 110, it follows that this is the limit for 
the voltage of the system. On the other hand, where the 
distribution is for power only and not for lighting, or where 
transformers can be used, the limit to the voltage is fixed by 
the entirely different consideration of the insulation which 
can be safely relied upon. 

Hence, to answer the question just raised we must dis¬ 
tinguish broadly between the two classes of systems and con¬ 
sider each on its own merits. 

1. High-pressure Systems .—In a high-pressure system it 
is the difficulty of devising an insulation that will not break 
down which practically limits the voltage. Therefore, in 
comparing polyphase and single-phase we must take cases 
that are on a par from this point of view of insulation. It has 
been common in the case of single-phase (and also in that of 
continuous currents) to keep one line at the potential of the 
earth, and to insulate the other sufficiently, having regard to 
the pressure between the two lines. In this case it is clearly 
the maximum pressure between the lines that forms what 
we here are calling the voltage of the system. If, however, 
both the lines are independently insulated from earth so 
as to withstand safely the maximum pressure occurring 
between line and earth, then the lines may have between 
themselves a voltage equal to double that maximum pressure 
without fear of a breakdown, provided always the lines, and 
the respective circuits into which they lead, are so well 
insulated from one another as to obviate risks in this respect. 
The question then arises whether, in comparing the advan¬ 
tages of various systems, we shall take as the basis of com- 


55 


Combinations of Polyphase Currents . 

parison the pressure between any two lines or the pressure 
between line and earth. If we take the maximum pressure 
between any point of the line and earth as the basis of com¬ 
parison, then there is no saving in copper by the employment 
of polyphase currents; for each line of any system, carrying a 
certain current at the maximum allowable pressure above the 
earth may be considered as dependency transmitting a certain 
amount of power; and therefore the total power is simply 
proportional to the number of line-wires, to which the total 
weight of copper is also proportional. 

For instance, a 3-phase system joined up in star fashion 
with the common junction to earth, and having a pressure 
of 1000 volts between each line and earth (and there¬ 
fore 1732 volts between line and line), has no advantage 
so far as the insulation of the line is concerned, over a single¬ 
phase system having a pressure of 1000 volts between each 
line and earth (and therefore 2000 volts between line and 
line). To transmit equal power, with equal loss in the lines, 
each of the two wires of the single-phase system must be 
li times as heavy as each of the three wires of the 3-phase 
system. The two systems will require equal total weights 
of copper. 

If, on the other hand, we take the maximum pressure 
between any two lines as the basis of comparison, we are now 
equating not the risks of breakdown of the lines, but the 
risks of breakdown of the apparatus, machines, transformers, 
etc., in which the goodness of the insulation must be con¬ 
sidered equal. And on this basis of comparison there is a 
decided economy of copper by the employment of 3-pliase 
currents, as can be seen by the following considerations. 

Taking first an installation connected in mesh fashion 
(Fig. 56, p. 47), if the distribution is symmetrical the current 

a in one limb of the mesh (see Fig. 160, p. 187) is —?— of 

^/ o 

the current p in the line (see p. 50). Therefore the power 

absorbed in one limb is —i- p V, where V is the pressure 
\t o 

between the lines (p and V being measured in virtual 
amperes and virtual volts respectively). The total power 


56 


Polyphase Electric Currents . 


is therefore ys p V. Taking instead a star connec¬ 
tion, the pressure between the ends of one branch of 


the star is 



and the current in each branch is the 


same as the current in the line. Therefore the total power 
is as before, viz. y^pV. Let the resistance of one line 
be r, then the total loss of power in the three lines is 3 p 2 r. 
Now consider a single-phase system to transmit the same 
amount of power y 3 p V. Let x be the resistance of one 
line, such that there shall be the same loss 3 p 2 r. The total 
resistance of the two lines will be 2 x. The current will be 
y 3p, and the loss 6 p 2 x. Hence 6 p 2 x = 3 p 2 r ; or x — \ r. 
The resistance of one of the two single-phase lines will have 
to be one-half the resistance of one of the three-phase lines. 
Or, to put it in another way: the single-phase system requires 
two wires, each of double cross-section, as against the three 
wires of the 3-phase system. The weight of copper required 
on the 3-phase system is only three-fourths of that required 
by any single-phase system. 

A 2-phase system with four wires is exactly on a par 
with a single-phase system, so far as the economy of copper is 
concerned. 

If in a 2-phase system only three wires are used, one 
wire acting as a common return, the pressure between the two 
outgoing lines is about y 2 times the pressure V between 
each line and the return ; we must therefore regard the voltage 
of the system as y 2 V. More copper is required in this case 
than for a single-phase transmission at y 2 Y. 

2 . Low-pressure Systems .—Here the pressure is limited 
by the requirements of incandescent lamps. What we wish 
to attain is to have the voltage between the lines that transmit 
the power as high as possible, consistently with keeping the 
pressure at the lamps terminals at the right amount. Putting 
aside for the moment the so-called three-wire and five-wire 


method of distribution in which balancing wires are used, 
and comparing 3-phase using three wires with single-phase 
using two wires, we see, from the considerations on p. 50, 
that with the lamps joined in mesh the 3-phase system 


Combinations of Polyphase Currents . 57 

has the advantage of using only 75 per cent, of the copper 
required for the single-phase system. If the lamps are 
connected in star fashion, we have the pressure between the 
lines |/ 3 times the pressure on the lamps, with a result that 
the copper employed is only one-fourth of that required for a 
single-phase system with two wires; but the system could 
not be regulated without having a return-wire from the 
common junction, and it would be comparable thus rather to 
a three-wire than a two-wire single-phase system. 

Mr. Goerges, in a paper read before the Elektrotech- 
nischen Verein, reprinted in the Elektrotechnische Zeitschrift, 
January 17,1895, gives the following data for weight of leads 
for equal power, drop and voltage :— 


For single-phase, 2 wires . 100 

44 single-phase, 3 wires (assuming the third wire half the ) 31*35 

section of the other) .> 

44 2 -phase, 4 wires. 100 

“ 2 -phase, 3 wires (reckoning the voltage between lines and ( ^*8 

common return) . 1 

“ 3-phase, 3 wires (mesh). 75 

44 3-phase, 4 wires (neutral wire from common junction) .. 29*2 


Another way of putting the matter is to consider the 
voltage to which the wires of a system would have to be 
raised in order, with equal total weights of copper in the lines, 
that equal power may be transmitted with equal loss. If 
a 3-phase system is arranged in star fashion with four 
wires, the voltage between any of the three lines and the 
neutral wire being reckoned as 1000, the voltage across the 
lines of a single-phase system to be equally efficient must be 
1850. It is here assumed that the system is balanced so that 
no current goes by the fourth wire. The extreme voltage 
from wire to wire in the 3-phase plant will be only 1732. 
If there is no fourth wire used in the 3-phase system (as 
need not be where motors only or transformers are to be sup¬ 
plied), the voltage of the single-phase system must, if it is to 
be equally efficient, be raised to 2000 volts. 







58 


Polyphase Electric Currents . 


COMBINATION OF MAGNETIC FIELDS. 

As the main object of polyphase working is to produce 
rotatory magnetic fields by the combining of alternating 
magnetic fields in different phases, it is appropriate now to 
consider how currents which are different in phases can be 
combined to produce resultant magnetic fields. 

We may take it that when a simple alternating current is 
carried in a coil around a core, the magnetism along that core 
will be an alternating magnetism. If the core is merely air, 
we shall have an alternating field. If the core is of iron, the 
flux of magnetic lines through it will be an alternating flux ; 
that is to sa}~, a flux which begins, increases to a maximum, 
then dies away, reverses in direction, increases to a reversed 
maximum, and dies away to begin the cycle over again. The 
frequency of this alternating flux will be the same as that of 
the impressed magnetomotive-force; that is to say, of the 
current. If the iron is properly laminated, and there are no 
secondary circuits to perturb by reactions, the rise and fall of 
the magnetic flux will be practically in phase with that of 
the surrounding current. Any eddy-currents in the core, and 
any secondary currents induced by the core in neighboring 
conductors, will inevitably have the effect of retarding the 
phase of the alternating magnetic flux, and of causing it 
to lag. Such reactions by induced currents in closed secondary 
circuit plays a vitally important part, as we shall see, in the 
modern polyphase motor. 

It is self-evident that (in the absence of secondary re¬ 
actions) a magnetizing force which alternates along a fixed 
direction will produce an alternating magnetic flux ; whereas 
a magnetizing force which is constant in value, but is continu¬ 
ously changing in direction—rotating in space—will tend to 
produce a rotating magnetic flux. Whether this resulting 
rotating magnetic flux will have a constant value or a uniform 
speed of rotation, will depend not only upon the uniformity of 
the impressed rotatory magnetizing force, and on the absence 
of secondary currents, but will also depend on the shape of the 
magnetic masses, as to whether they also are magnetically 


Combinations of Polyphase Currents . 59 

symmetrical around the axis of rotation of the magnetizing 
forces. 

For the present, to gain simplicity in grasping the subject, 
we will consider the problem of the combinations of magnet¬ 
izing forces to produce a resultant magnetizing force. 

If the direction and intensity of a magnetic field may be 
represented by the direction and length of a line, then we may 
apply the ordinary parallelogram rule for the compounding 
of vectors, and find the resultant of two magnetic fields that 
differ in direction and magnitude by compounding the vectors 
that represent them, and drawing the diagonal. In cases 
where the two components have values that vary in a regular 


R 



periodic manner, the questions arise whether they have the 
same period of variation, and what is the difference between 
their phases. Consider for example two components A and B, 
the directions of which are fixed, but of which the magnitudes 
can vary. Take the case first (Fig. 68) in which they vary 
together without any difference of phase. When component 
A has the small value O A x and component B the small value 
O B x , the resultant will be O R x . When A grows to O A 2 and 
B to O B 2 the resultant will be O R 2 ; and it is evident that if 
the magnitudes of O A and O B increase and decrease together, 
the resultant O R will also vary in the same phase, but will 
remain fixed in its own direction. In brief, two alternating 
vectors of equal period and in identical phase have as their 




6o 


Polyphase Electric Currents . 

resultant another alternating vector of equal period, identical 
phase, and of fixed direction. 

If, however, as in Fig. 69, the two components go through 
their periodic changes with a difference between their phases, 
not increasing and decreasing together, the resultant will no 
longer have a fixed direction. Let the variations of A and B 
be such that when O A is large, O B is small, and that while 
O A decreases O B increases. Then it is evident that the 
resultant will change, as in the figure, from O R x to O R 2 , O R 3 
&c.; and, if the variations of the two components follow the 
proper law , the resultant may be caused to change continuously 
in direction without changing in magnitude; or, in other 
words, two alternating vectors may be arranged to have as 
their resultant a rotating vector of constant value. What 
the law must be to produce this effect we must next see. 

In 1883 1 Marcel Deprez communicated to the Academic 
des Sciences an important theorem on the production of a true 
rotatory magnetic field, by the combination of two alternating 
magnetic fields having as their difference of phase a quarter 
period. 

It is well known that a uniform circular motion can be 
decomposed into two rectilinear harmonic motions at right 
angles to one another, the two having equal amplitude, equal 
period and a phase difference of one-quarter period. Let P 
be a point uniformly revolving around centre O. The pro¬ 
jections of the radius O P upon the two axes (Fig. 70) are 
O M and ON. If the radius O P be called r we have O N = 
r sin 0, and O M = r cos 0 = r sin (0 + 90°). While P re¬ 
volves the point N will oscillate up and down the line Y Y'; 
the amplitude of its motion being equal to the radius of the 
circle. Also the point M will oscillate along the line X X' 
with equal amplitude and in equal time; but O N will be at 
its maximum when O M has zero value, and vice versa . It 
follows kinematically that a uniform circular motion may be 
produced out of two straight-line motions, by combining them 
at right angles, provided they are harmonic, of equal period, 
of equal amplitude and differing by an exact quarter period. 

1 Comptes Rendus , 1888, II. 1193. 


Combinations of Polyphase Currents. 61 

Mechanically this motion is equivalent to that of two 
pistons having equal travel, working by two connecting rods 
upon the same crank pin, but placed at right angles to one 
another (Fig. 71). If motion of rotation is given to the shaft 
it will be decomposed into two rectilinear motions; the appa¬ 
ratus then acting as a two-throw pump. If on the other hand 
the cylinders are made to produce two rectilinear motions one 
ahead of the other by a quarter period in time, the apparatus 
will combine these motions into a true circular motion, and be¬ 
comes equivalent to a two-crank engine with parallel cylinders. 

Deprez saw that a similar combination can be magneti¬ 
cally effected. If an alternating current is led around a coil so 



as to produce an alternating or oscillating magnetic field along 
the line O X, and a second alternating current is led round a 
second coil so as to produce a second alternating magnetic 
field along the line O Y, then the result will be a rotatory 
magnetic field, provided these two magnetic fields are of equal 
period and amplitude, and differ exactly a quarter in phase. 
If they are of equal period, but not of exactly equal amplitude, 
the result will be equivalent to an elliptically -rotating magnetic 
field; that is to say, one in which the strength and direction of 
the field is represented by the successive values of the radius 
vector drawn to an ellipse from its centre, and sweeping over 
equal areas in equal times. An elliptically rotatory field will 






















62 


Polyphase Electric Currents. 

also be produced if the two component magnetic fields, though 
equal in period and amplitude, do not differ by exactly a 
quarter period. For a perfect rotatory field, corresponding 
to uniform circular motion, the two components must vary 
precisely as the sine and the cosine 1 of an angle respectively. 

This is not by any means the only combination that will 
produce a rotatory magnetic field. The mechanical analogues 
of the three-crank engine, and of the three-throw pump, at 
once suggest other solutions. In the former instance three 
cylinders are used, with three pistons which operate in succes¬ 
sive phases differing by one-third of a period from one another. 
If the three cylinders are set (as in a Brotherhood’s engine) at 
120° to each other, their connecting-rods may actuate a single 
crank. If the three cylinders are set parallel side by side, 
then there must be three cranks spaced out in angular posi¬ 
tions 120° from one another. If the angular positions of the 
cranks were not exactly 120° apart, the phase-differences of 
the motions will not be exactly one-third of the period. The 
phase-difference of the motion must correspond to the peri¬ 
pheral spacing of the mechanism that combines them. It 
is a kinematic principle that in combining harmonic motions 
to produce rotation, the space-phase of angle in the combining 
mechanism must be the supplement of the angle which repre¬ 
sents the time-phase of motion, otherwise the resulting motion 
will not be a uniform rotation. 

The famous three-phase system of currents (or drehstrom ) 
for producing a rotatory magnetic field, is the electrical 
analogue of the three-crank mechanism. In dealing with such 
combinations of magnetic fields, we may proceed analytically. 
We have three coils, or three pairs of coils, each producing a 
component magnetic field which alternates along a fixed 
direction, and we want to find the resultant field when they 
are combined together. When the coils are placed at an 
angle to each other we have to take into account not only the 
strength of each component field determined by the phase of 
the current, but also the direction of it. This is most easily 
done by splitting up the field produced by each circuit into 
i See also Ferraris, “Rotazioni elettrodynamiche,” Turin Acad., March 1888. 


Combinations of Polyphase Currents . 63 

components along two axes X and Y. For instance, taking 
the coils on the ring in Fig. 58, the coils b and e will together 
produce a horizontal flux in the direction of O b along the axis 
of X in Fig. 72, which will change in value following the law 
H sin 0. The coils d and a will produce a field in the direction 
of O d which will follow the law H sin ($ —120°). Similarly 
the coils / and e will produce a flux in direction Of following 
the law H sin (0— 240°). 



Adding together the components of these along the axis 
of X we get 

|_| s i n 0—\-\ sin (0—120°) cos 60°—H sin (0—240°) cos 60 

= — H sin 0. 

2 

And taking the components along the axis of Y. 

H sin (0—240°) cos 80 — H (sin 0 —120°) cos 80 =|h cos #• 

3 

If we draw a line O R representing Y H to scale, making 

the angle 0 with the axis of Y we shall see that as 0 increases 
with time and R revolves round O, the projection of O R 

upon the axis of X is — I - 1 sin 0, and on the axis of \ it is 
-H cos 0. Therefore O R represents the direction of the 






6 4 


Polyphase Electric Currents . 


resultant of the field at any moment. The field has, there¬ 
fore, a constant value equal to one and one-half times the field 
produced by one pair of coils, and rotates at a constant 
angular velocity. 

Generally we may say that with a symmetrical grouping 
of coils, if the number of phases is called m, the ratio of the 

resultant field to the field produced by one phase 

We see, then, what are the time and space relations in 
simple 2-phase and in simple 3-phase working. To produce 
a uniformly rotating magnetic field, we may have as com¬ 
ponents either two equal fields differing by a quarter-period 
in time, and set at 90° (i. e. a quarter circumference) to 
one another in space; or, instead, three equal fields differing 
by a third of a period from one another in time, and set 
mutually at 120° (i. e. a third of a circumference) to one 
another in space. Obviously other cases might arise. Refer¬ 
ence to Fig. 71, p. 61, will show that by simply putting the 
two cylinders at some other angle than a right angle, uniform 
circular motion might be resolved into two simple harmonic 
motions of equal period which did not differ by a quarter 
period. It was stated on p. 62 that a uniform circular motion 
may be recompounded out of two equal simple harmonic 
motions that do not differ by a quarter period, provided the 
space-phase of their angular positions is equal to the sup¬ 
plement of the time-phase of their motions. 

We may very briefly discuss those cases where the time- 
phase of the components does not correspond to the space- 
phase of their angular positions. In such cases the result is 
not uniform circular rotation ; it becomes, in fact, elliptical. 
The resultant, while revolving, does not revolve at a uniform 
angular speed, nor maintain an invariable magnitude. The 
cases of elliptical resultant rotation may be classified under 
several heads. If the two component simple-harmonic motions 
are equal in amplitude and of equal period, but not set in 
such relative positions that the angle between them in space is 
the supplement of the phase-difference between them in time, 
the resultant motion will be elliptical, not circular. If the two 


Combinations of Polyphase Currents. 65 

components, of equal period, and having angular positions 
supplemental to the phase-difference between them in time, 
are not equal in amplitude, there will result elliptical motion, 
and the major axis of the ellipse will coincide with the direc¬ 
tion of the component of greater amplitude. If the phase- 
relations are not supplemental, and the amplitudes of the two 
components are unequal, yet the resultant motion will still 
be elliptical if the periods of the harmonic components are 
equal. Hence it follows that the resultant of any three (or 
more) simple harmonic components of equal periods, whatever 
their amplitudes and whatever the relations between their 
mutual angles and their phase-relations in time, will be an 
elliptical rotation (including in that general case the two 
special cases of rectilinear simple-harmonic motion, when the 
time-phases of all components are alike, and of uniform circu¬ 
lar motion when the components are equal in amplitude and in 
time-phase relations corresponding to their angular differences 
in space). This is why unsymmetrical polyphase systems, 
such as the so-called “ monocyclic” system (which is a dis¬ 
torted three-phase system) will drive motors about as well as 
a symmetrical system will do. 

Returning to the case of 2-phase and 3-phase combinations 
properly so-called, it may be remarked that even though the 
amplitudes of the components are equal and their phase re¬ 
lations are properly adjusted, the result cannot be a uniform 
circular motion unless the individual components are truly 
harmonic—that is to say, follow exact sine functions. Now 
we know that in many cases 1 the form of the curves of electro¬ 
motive-forces, currents and magnetomotive-forces in the actual 
alternating current systems in use differs considerably from 
that of a simple sine curve. It is easy to see in general what 
will be the effect of any departure from the simple sine form. 
Taking a 2-phase combination, if the component curves are of 
the peaked type, the resultant curve will have the general 
form of Fig.73, while if the component curves are of the broad- 
topped round-backed variety, the resultant will have the 

1 See for a recent example, the curves given by Fleming in The Electri¬ 
cian of February 22d, 1895, for some alternators used in the City of London. 

5 


66 


Polyphase Electric Currents . 


general form of Fig. 74. If one or both the curves present a 
rippled outline owing to the presence of a sub-component of 
higher order of periodicity, the contour of the resultant curve 
will also be rippled. This corresponds to the entirely unim¬ 
portant case of a motor designed to work with a rotatory mag¬ 
netic field with the amplitude of the resultant magnetic force 
undergoing more rapid periodic fluctuations. 

In the paragraphs immediately preceding, the combination 
of component vectors has purposely been discussed from the 
rather abstract or kinematic point of view. The rotatory 
phenomena in the polyphase motors are both more concrete 



and more complex. In them the impressed magnetic field 
seldom has a simple uniform circular rotation. They are 
mostly multipolar; they have projecting poles, teeth and 
other discontinuities of structure, all of which must have a 
tendency to cause the magnetic field to rotate more or less 
by jumps, and with variations in its magnitude from point to 
point. This is, however, of minor importance, for, as we shall 
see, the necessary tendency of the induced effects in the 
conducting revolving masses is to react against all departures 
from simple and uniform rotation. Further, in the ideal case, 
what is sought is not a uniformly rotating magnetic field, but 
such a combination of rotating magnetic field with a set of 










Combinations of Polyphase Currents. 67 

induced currents that the conductors carrying the latter (or 
the iron core in which they are embedded) shall be urged 
around its axis with a sufficient and sufficiently uniform 
torque. The torque at different points of the revolution is 
not uniform in steam engines, even in those provided with 
two and three cranks. But even in the worst polyphase 
motor the torque is much more uniform than in the best 
steam engine. No polyphase motor, no single-phase motor 
even, needs any fly-wheel to regularize the irregularity of the 
turning effort. 

Lastly, it may be well to remind the student that the 
principle of vector combination (such as in the well-known 
parallelogram of vectors) is only applicable to magnetomotive- 
forces, magnetic fluxes, and electric currents when we are 
considering these quantities as vectors, that is to say when 
their actual direction in space is being taken into account, 
and, therefore, obviously cannot be employed in dealing with 
quantities of a circuital nature such as the total magneto¬ 
motive force, or as the total magnetic flux in a circuit, or 
in combining currents flowing from several wires into a 
common wire. There the quantities in question have merely 
a scalar value; their directions varying throughout their 
circuit. If we are considering the magnetic force at a point, 
we have something with a perfectly definite direction, and 
may, therefore, combine it with another magnetic force at 
the point. Similarly, when we are considering magnetic fields 
whose directions at a particular instant are uniform over the 
space we are considering, as in the case of the magnetic fields 
in the theorem of Marcel Deprez on p. 60, and the theorem 
which follows it, as to the resultant field in a particular 
three-phase motor, the principles of vector combination are 
applicable. But in a multipolar motor, where the flux is 
along curved paths, as shown In Figs. 24 and 125, the flux as 
a whole cannot be considered as a vector, and it is for this 
reason that in Chapter V., in the discussion of the progression 
of the magnetic field, the diagrams have been drawn to show 
how the circuit magnetomotive-forces progress peripherally 
along the motor. 


68 Polyphase Electric Currents . 

The student must clearly distinguish between the applica¬ 
tion of the polygon of vectors in the case where vector 
quantities are being added, and the application of the same 
geometrical construction when scalar quantities, following a 
sine function of the time, are being added. In the latter case 
the quantities have their phase relations represented by the 
inclination of lines to one another; the legitimacy of the 
process depending solely upon the peculiar properties of the 
sine functions. 


Properties of Rotating Magnetic Fields. 


CHAPTER III. 

PROPERTIES OF ROTATING MAGNETIC FIELDS. 

Considering how much attention has been devoted to 
magnetic fields and to the combinations of the fields of two 
or more magnets, it is surprising how little thought has been 
given to the properties of rotating magnetic fields. The 
essence of the modern polyphase motor is the production of 
rotating magnetic fields within which masses of metal are set 
into forcible rotation by reason of the currents induced in 
them. These rotating magnetic fields are generated by the 
artifice of combining together two or more oscillating magnetic 
fields by the use of alternate currents in different phases, as 
already shown. But the principal properties of rotatory fields 
can be investigated and demonstrated without any such 
artifices, by very simple means. All that is required is an 
apparatus for spinning a magnet, the field of which is then 
investigated while it revolves at some known speed. 

The subject appears to have first attracted notice about 
the year 1825, in the discussion of the phenomenon of Arago’s 
rotations, of which, accordingly, some is here given. 

Arago's Rotations .— As has so often occurred in other 
branches of science, the discovery of the magnetic rotations 
was made nearly simultaneously by several persons, for all of 
whom priority has been claimed. About 1824, Gambey, 1 the 
celebrated instrument-maker of Paris, had made the casual 
observation that a compass-needle, if disturbed, and set oscil¬ 
lating around its pivot, comes to rest sooner if the bottom of 
the compass-box is of copper than if it is of wood or other 
material. Barlow and Marsh, 2 at Woolwich, had at the same 

1 See Jamin, Cours de Physique, iii. 296, 1869, and Yerdet, Conferences 
de Physique , i., 415 1872. 2 Edinburgh Philos. Journal , xiii. 122, 1825. 


70 


Polyphase Electric Currents . 

time been observing the effect on a magnetic needle of 
rotating in its neighborhood a sphere of iron. Arago, 1 the 
astronomer, who is said to have learned of the phenomenon 
from Gambey, but who is also said 2 to have independently 
discovered it in 1822, when working with Humboldt at mag¬ 
netic determinations, was beyond question the first to publish 
an account of the observation, which he did verbally before 
the Academie des Sciences of Paris, on November 22d, 1824. 
He hung a compass-needle within rings of different materials, 
pushed the needle aside to about 45°, and counted the number 
of oscillations made by the needle before the angle of swing 
decreased to 10°. In a wooden ring the number was 145, 
in a thin copper ring 66, and in a stout copper ring it was 
only 88. 

The effect of the presence of the mass of copper is to 
damp the vibrations of the needle. Each swing takes the 
same time as before, but the amplitudes are lessened; the 
motion dying down, as though there were some invisible 
friction at work. Arago marked that it gave evidence of 
the presence of a force which only existed whilst there was 
relative motion between the magnet-needle and the mass of 
copper. He gave the phenomenon the name of magnetism 
of rotation. In 1825 he published a further experiment, in 
which, arguing from the principle of action and reaction, 
he produced a reaction on a stationary needle by motion of a 
copper disk (Fig. 75). Suspending a compass-needle in a 
glass jar closed at the bottom by a sheet of paper or of glass, 
he held it over a rotating disk of copper. If the latter turns 
slowly the needle is simply deviated out of the magnetic 
meridian, tending to turn in the sense of rotation of the disk, as 
though invisibly dragged by it. With quicker rotation the 
deviation is greater. If the rotation is so swift that the needle 
is dragged over 90° a continuous rotation ensues. Arago found, 
however, that the force was not simply tangential. Suspend¬ 
ing a needle vertically from the beam of a balance over the 
revolving disk he found that it was repelled when the disk was 

1 Annales de Chimie et de Physique, xxvii. 363, xxviii. 325, xxxii. 213. 

2 Arago, (Euvres completes, iv. 424. 


Properties of Rotating Magnetic Fields. 71 

revolved. The pole which hung nearest the disk was also 
acted upon by radial forces tending, if the pole was near the 
edge of the disk, to force it radially outward, but if the pole 
was nearer the centre, tending to force it radially inward. 

Poisson, steeped in Coulomb’s notions about magnetic 
action at a distance, essayed to build up a theory of mag¬ 
netism of rotation, affirming that all bodies 
acquire a temporary magnetism in the 
presence of a magnet, but that in copper 
this temporary magnetism took a longer 
time to die away. In vain did Arago point 
out that the theory failed to account for 
the facts. The so-called “ magnetism of 
rotation ” threatened to become a fixed 
idea. 

At this stage the phenomenon was 
investigated by several English experi¬ 
menters, by Babbage and Herschel, by 
Christie, and, later, by Sturgeon and by 
Faraday. Babbage and Herschel measured 
the amount of retarding force exerted on 
the needle by different materials, and found 
the most powerful to be silver and copper 
(which are the two best conductors of 
electricity), after them gold and zinc, whilst lead, mercury 
and bismuth were very inferior in pow r er. In 1825 they 
announced the successful reversal of Arago’s experiment ; 
for by spinning the magnet underneath a pivoted copper 
disk (Fig. 76) they had caused the latter to rotate briskly. 
They also made the notable observation that slits cut 
radially in a copper disk (Fig. 77) diminished its tendency 
to be rotated by the spinning magnet. If the rotatory force of 
the unslit disk be reckoned as 100, one radial slit reduced it to 
88, two radial slits to 77, four to 48, and eight to 24. Ampere, 
in 1826; showed that a rotating disk of copper also exercises 
a turning moment upon a neighboring copper wire through 
which a current is flowing. Seebeck in Germany, Provost 
and Colladon in Switzerland, Nobili and Bacelli in Italy, con- 



Fig. 75.—Arago’s 
Spinning Disk. 






























72 Polyphase Electric Currents . 

firmed the observations of the English experimenters, and 
added others. Sturgeon showed that the damping effect of a 
magnet pole upon a moving copper disk was diminished by 
the presence of a second magnet pole of contrary kind placed 
beside the first. Five years later he returned to the subject 
and came to the conclusion that the 
effect was an electrical disturbance, 
“ a kind of reaction to that which takes 
place in electro-magnetism,” when the 
publication of Faraday’s brilliant re¬ 
search on magneto-electric induction, 
in 1831, forestalled the complete ex¬ 
planation of which lie was in search. 
Faraday, in fact, showed that relative 
motion between magnet and copper 
disk inevitably set up currents in the 
metal of the disk, which, in turn, 
reacted on the magnet pole with 
mutual forces tending to diminish the 
relative motion—that is, tending to 
drag the stationary part (whether magnet or disk) in the 
direction of the moving part, and tending always to oppose 
the motion of the moving part. In fact, the currents go 
eddying round in the moving disk, unless led off by sliding 
contacts. This, indeed, Faraday effected, when he inserted 



Fig. 76.— Barrage and 
Herciiel’s Experiment. 



Fig. 77.—Slit Disks used by Babbage and Herschel. 

his copper disk edgeways (Fig. 78) between the poles of 
a powerful magnet, and spun it, while against edge and axle 
were pressed spring contacts to take off the currents. The 
electromotive-force, acting at right angles to the motion, and 
to the lines of the magnetic field, produces currents which 










Properties of Rotating Magnetic Fields . 73 

flow along tlio radius of the disk. If no external path is pro¬ 
vided, the currents must find for themselves internal return 
paths in the metal of the disk. Fig. 79 shows the way in 



Fig. 78.— Faraday’s Disk Machine. 


which a pair of eddies is set up in a disk revolving between 
magnet poles. These eddies are symmetrically located 1 on 
either side of the radius of maximum electromotive-force 



Fig. 79.—Eddy-currents in 
Spinning Disk. 



Fig. 80.— Paths of Eddy- 
currents. 


(Fig. 80). The direction of the circulation of eddy-currents 
is always such as to tend to oppose the relative motion. The 
eddy-current in the part receding from the poles tends to attract 

1 Unless the speed of the rotation is very great; in which case the self-in¬ 
duction of the eddy-circuits will cause a time-lag shifting the position of the 
radius of maximum current ahead of the radius of maximum electromotive- 
lorce. 

















74 


Polyphase Electric Currents. 


the poles forward or to drag this part of the disk backwards. 
The eddy-current in the part advancing toward the poles 
tends to repel those poles and to be repelled by them. It is 
obvious that any slits cut in the disk will tend to limit the 
flow of the eddy-currents, and by limiting them to increase 
the resistance of their possible paths in the metal, though it 
will not diminish the electromotive-force. In the researches 
of Sturgeon 1 a number of experiments are described to ascer¬ 
tain the directions in which the eddy-currents flow in disks. 
Similar, but more complete researches were made by Matteuci. 
The induction in rotating spheres was mathematically inves¬ 
tigated by Jochman, and later by the lamented Hertz. 



Fig. 82. 


Fig. 81. 


Faraday showed several interesting experiments on eddy- 
currents. Amongst others he hung from a twisted thread a 
cube of copper in a direct line between the poles of a powerful 
electromagnet (Fig. 81). Before the current was turned on 
the cube, by its weight, untwisted the cord and spun rapidly. 
On exciting the magnet by switching on the current, the cube 
stops instantaneously ; but begins again to spin as soon as 
the current is broken. Matteucci varied this experiment by 
constructing a cube of square bits of sheet copper separated 
by paper from one another. This laminated cube (Fig. 82) 
if suspended in the magnetic field by a hook a, so that its 
laminse were parallel to the lines of the magnetic field, could 
not be stopped in its rotation by the sudden turning on of the 
current in the electromagnet ; whereas if hung up by the 
hook b, so that its laminations were in a vertical plane, and 

1 Edinburgh Philosophical Journal , July 1825 ; and. Philosophical Maga¬ 
zine, April and May 1832. See also Sturgeon’s Scientific Researches, p. 211. 













Properties of Rotating Magnetic Fields . 75 

then set spinning, was arrested at once when the electro¬ 
magnet was excited. In the latter case only could eddy- 
currents circulate ; since they require paths in planes at right 
angles to the magnetic lines. 

With the explanation given by Faraday of the Arago 
rotations, as being merely due to induced eddy-currents, the 
peculiar interest which they excited whilst their cause was 
unknown, seems almost to have died out. True, a few years 
later some interest was revived when Foucault showed that 
they were capable of heating the metal disk, if in spite of the 
drag the rotation was forcibly continued in the magnetic field. 
Why this observation should have caused the eddy-currents 
discovered by Faraday as the explanation of Arago’s pheno¬ 
menon to be dubbed Foucault’s currents is not clear. If any 
one is entitled to the honor of having the eddy-currents 
named after him, it is obviously Faraday or Arago, not 
Foucault. A little later, Le Roux produced the paradox that 
a copper disk rotated between concentric magnet poles is not 
heated thereby, and does not suffer any drag. The explana¬ 
tion of this is as follows. If there is an annular north pole 
in front of one face of the disk, and an annular south pole in 
front of the other face, though there is a magnetic field pro¬ 
duced right through the disk, there are no eddy-currents. 
For if all round the disk there are equal electromotive-forces 
directed radially inwards or radially outwards, there will be 
no return path for the currents along any radius of the disk. 
The periphery will simply take a slightly different potential 
from the centre ; but no currents will flow because the electro¬ 
motive forces around any closed path in the disk are balanced. 

In 1884, Willoughby Smith published 1 an investigation on 
rotating metal disks in which he found iron disks to generate 
electromotive-forces superior to those generated in copper 
disks of equal size. 

Guthrie and Boys in 1879, 2 hung a copper plate over a 
rotating magnet by means of a torsion thread, and found that 

1 Lecture at Royal Institution: “ Yolta and Magneto Electric Induction,” 
June 1884. 

2 Proc. Physical Soc ., iii. pt. iii. 127, and iv. 55. 


76 Polyphase Electric Currents . 

the torsion was directly proportional to the velocity of rota¬ 
tion. They pointed out that such an instrument was a very 
exact one for measuring the speed of machinery. They also 
made experiments upon varying the distance between the 
copper plate and the magnet, and varying the diameter and 
thickness of the copper disk. 

Experiments were made upon various metals, and the 
torque was found to vary as the conductivity of the metal as 
far as the latter could be judged after being rolled into the 
form of plate. Messrs. Guthrie and Boys then applied the 
method to the measurement of the conductivity of liquids. 

In 1880, De Fonvielle and Lontin observed that a lightly 
pivoted copper disk could be maintained in continuous rota¬ 
tion—if once started—by being placed, in presence of a 
magnet, within a coil of copper wire wound on a rectangular 
frame (like the coil of an old galvanometer), and supplied with 
alternate currents from an ordinary Ruhmkorff induction coil. 
They called their apparatus an electromagnetic gyroscope. 

But it does not seem to have occurred to any one that the 
Arago rotations could be made use of in the construction of 
a motor prior to the year 1879 (see p. 84). 

Experiments in a Rotating Magnetic Field .—With the 
simple apparatus of Fig. 76 a number of interesting and easy 
experiments can be shown. A pivoted compass-needle 
placed over the magnet revolves synchronously. If a number 
of small “ charm ” compasses are placed close together over 
the revolving magnet, they all turn together in unison. Any 
pivoted disk of thin sheet iron (ferrotype plate or tinned- 
ware), also rotates synchronously. An iron nail or a steel pen 
laid on a sheet of glass over the magnet begins to revolve as 
soon as the magnet is turned, and will acquire a great speed, 
turning always synchronously with the magnet. So will a 
small iron key; but if the magnet is first spun very quickly 
and the iron nail or key is then laid down on the glass, it fails 
to fall into step, and does not turn. If iron filings are 
sprinkled from a pepper-box upon the glass sheet (a sheet of 
mirror glass is preferable) over the slowly revolving poles, a 
very curious and beautiful effect is produced. Owing to the 


Properties of Rotating Magnetic Fields. 77 

magnetic fields proceeding from the poles having vertical 
components, each tuft of filings rises up on end as the poles 
pass under, and turns a complete somersault at each rotation 
of the magnet. By each somersault the tufts of filings are 
shifted a little in a sense contrary to that of the rotation; 
giving, as the speed is increased, the effect of particles waltz¬ 
ing round in a flock, and gradually tending either to heap 
together in the centre or to drift out of the field at the edges 
of the sheet of glass. Iron bullets or buttons revolve syn¬ 
chronously with the magnet. Bullets or egg-shaped pieces of 
copper or brass revolve quite slowly however, and do not keep 
pace with the revolving magnet, as do bodies of magnetic 
material. Pivoted disks of copper, brass, zinc, or, best of all, 
of aluminium, placed over the magnet, also take up a slow 
non-synchronous revolution, being driven by the eddy currents 
generated in them. 

If the pivoted disks, compass needles and the rest are how¬ 
ever, not placed centrally over the moving magnet, but are 
set at some distance laterally, quite outside the sweep of the 
moving poles, the rotation produced in the pivoted disks is 
in a sense opposite to that of the rotation of the magnet. If 
the pivoted disk is set centrally over the revolving magnet at 
a height of 6 or 8 inches above its poles, and is gradually 
moved laterally away from this central situation, a point may 
be found at some distance where the disk does not tend to 
turn in either direction. Inside the zone of such neutral 
points the tendency is to revolve in the same sense as the 
magnet; outside that zone, to revolve in the opposite sense. 
The neutral zone widens as the vertical distance is increased. 
If a pivoted disk is set at a neutral place, it may be made to 
revolve by placing in the interspace pieces of iron or even 
strips or hoops of copper in positions which either distort the 
field or convey by eddy-currents a new revolving field. If a 
conducting cage of copper strip, made up like Fig. 83, is set 
up over the revolving magnet, and a well-pivoted disk of 
aluminium is placed over the top of it at this disk may be 
set in rotation, though the distance between the magnet and 
the disk is far too great for rotation to be set up without this 


7 « 


Polyphase Electric Currents . 



adjunct. The effect is improved by inserting a mass of iron 
at b to increase the inductive effect of the revolving magnet. 

Another instructive experiment, shown by the author at 
the Royal Institution in February 1894, is afforded by cutting 
out a piece of sheet copper in the form shown in 
Fig. 84, having two long slits running nearly the 
whole length. This may be several feet long, 
and three or four inches broad. If the strip is 
laid down horizontally, with the point A cen¬ 
trally over the revolving magnet, with a block 
of iron over it to enhance the inductive action, 
eddy-currents are set up in the strip (in reality 
3-phase eddy-currents) which are able to turn a 
nicely poised metal disk placed on a pin at the 
distant end B. The disk used in this experiment 
consisted of a copper disk having a thickened 
rim, with a smaller iron disk laid within the rim, the whole 
being provided with a jewelled centre to diminish friction. 
All these effects can be produced with much greater power 




Fig. 83. 



Fig. 84. 


by substituting for the mechanically-turned steel magnet any 
apparatus producing a rotatory field by the combination of 
true polyphase currents as described later on. 

For those who have no true polyphase apparatus at their 
command, but who have batteries capable of furnishing 5 to 
10 amperes at a pressure of 10 to 20 volts or more, it may be 
convenient to describe a method of artificially imitating true 
polyphase currents by means of a hand-driven commutator. 

Fig. 85 shows a very simple form of commutator, by which 
a rotating field can be produced if the terminals A, B and C 
are connected to the terminals m, o and n of a ring wound as 
in Fig. 58, p. 48, and a battery is connected by one pole to 
the return terminal R of the commutator, and the other pole 




















Properties of Rotating Magnetic Fields . 79 

to the common junction J of the coil. On turning the handle 
rapidly the three contact springs receive currents at successive 
intervals, which may be said to differ in phase by 120°, though 
of course there is no reversal. It will be seen that the intervals 
overlap by an angle of 60°; that is to say, the current in B is 
switched on £ of a period before the current in A is switched 
off, and for \ of a period current in B only is on, after which 
currents in B and C are both on for J of a period, and so on. 
The bearing surface of the teeth is one-half of the pitch, and 



Fig. 85.— Hand Commutator for Imitating Three-phase Currents. 

the tips of the contact springs virtually tri-sect the pitch. 
This commutator can be cut out of a single sheet of brass, 
and though soon spoilt by the sparking is easily repaired. 

A more elaborate commutator which reverses the currents 
in the three lines in proper succession, and does not require a 
fourth line as a return-wire, is shown in Fig. 86. It repre¬ 
sents a wooden barrel about 2 inches in diameter and about 
5 inches long, upon which are screwed two properly spaced 
contact-pieces. Against this barrel press springs ; three of 
these being terminals for the three lines; two to be joined to 



























8 o 


Polyphase Electric Currents . 

the terminals of the battery. A developed drawing of this 
commutator, showing how the contact pieces are spaced out, 
is given, exactly half the actual size, above the figure. 

By carefully following the order of operations during one 
revolution, it will be seen that the current is successively 





Fia. 86 .—Hand Commutator for Producing Three-phase Currents. 


reversed in each line and that while the current is flowing 
from a + terminal through the A line, the return current to 
a - terminal is shifted from the B line to the C line, and so 
forth in regular order. 





































































Properties of Rotating Magnetic Fields . 81 

A similar device (but, of course, with different spacing of 
the parts) may be used to imitate 2-phase currents, using 
four lines. This will require six springs, unless a common 
return is used. Indeed, the commutator just described works 
fairly well for 2-phase apparatus if the terminal C is used 
with a common return-line for the two circuits that go out 
from A and B. 

To show simple rotatory-field experiments with this three- 
phase commutator, all that is necessary is a ring electro¬ 
magnet properly wound. Take a ring-core made either of 
iron wire or of iron core-rings stamped from sheet iron, having 
an external diameter of 3 or 4 inches and an internal 
diameter of 2 or 3 inches. Its depth may also be half an 
inch or so. After insulating it with tape, or paper varnished, 
wind carefully upon it six equal coils of No. 16 S.W.G. covered 
copper wire (or stranded wire of 7 No. 23 S.W.G. for greater 
flexibility). Let the three coils each cover 60°. Their ends 
may be furnished with terminals, so that if desired they may 
be joined either in star fashion or in mesh fashion. Each 
coil should have at least 100 turns. If a finer wire is used 
(and it has some advantages) there must be a proportion¬ 
ately greater number of turns wound upon the ring. With 
a small ring such as this almost all the above experiments can 
be shown. 

For experiments on a larger scale, polyphase currents can 
be readily procured by those who have access to an electric 
lighting supply of continuous current. For it is easy to adapt 
a small motor to serve the purpose of a running transformer. 
Suppose the supply is at 100 volts. Then a small motor of 
1 horse-power, or even of £ or 4 horse-power, can readily be 
adapted to the purpose, provided there is room on its shaft 
at the end opposite to the commutator to adapt to it three 
insulated slip-rings which are connected to three symmetrical 
points on the armature winding. From these three slip-rings 
three contact-brushes take off the 3-phase current (p. 183). 

One of the most fascinating experiments which can readily 
be shown with such an apparatus is the spinning of a copper 
egg. For this purpose, a somewhat larger ring electromagnet 


82 


Polyphase Electric Currents. 

is required than that described above for producing the rotat¬ 
ing field. An 8-inch ring, wound in 6 or 12 sections, and 
connected up as in in Fig. 58 or Fig. 59, serves excellently. 
A ring wound in 12 sections (see Fig. 157, p. 180) is very 
convenient, since it can also be used for 2-phase currents. 
The ring is laid upon a table, and a common china plate may 



Fig. 87. 


be set upon it. An egg of copper, solid or hollow, or, better 
still, of copper filled with iron filings, revolves rapidly when 
the current is turned on. As its speed of rotation increases 
it finally rises up and spins on its end. An aluminium egg 
revolves even better. A stout disk of copper or aluminium, if 
slightly convex on the face, and rounded at the edges, spins 
and gradually rises up until it spins on its edge like a coin. 

MECHANICAL ILLUSTRATIONS OF POLYPHASE 
TRANSMISSION. 

The analogies between polyphase current apparatus and 
machines in which two cranks or three cranks are used so as 
to avoid dead-points, have been several times alluded to. 
Mechanical models corresponding to any particular case of 
polyphase currents can easily be designed, and are very in¬ 
structive. A very simple model designed by the author to 
illustrate a simple 8-phase transmission of power, may be 
worthy of record. 

Three cords are attached to a pin P on a small crank, 
rotating about centre O in the middle of a fixed board 







Properties of Rotating Magnetic Fields . 83 

(Fig. 88). The three cords are led off through three equi¬ 
distant holes A, B, C, furnished with porcelain eyelets to 
diminish friction. The three cords pass over three pulleys 
a, b, c to a distant point, where they are brought down to a 


b 





Jr 




l 






itJs 


Fig. 88. 


similar board and reunited at a common junction^, to which 
a pencil is fastened. On imparting a circular motion by 
hand to the handle h, the point p also performs a circular 
motion, though there is no crank to guide its motion, and 
traces an (approximate) circle on the board. 

Another method of mechanical illustration, using cords 
and pulleys, was devised by Mr. P. A. N. Winand (see 
Journal of the Franklin Institute, October, 1892). 
























8 4 


Polyphase Electric Currents . 


CHAPTER IV. 

EARLY DEVELOPMENT OF THE POLYPHASE MOTOR. 

The notion of producing rotation by using several magnet 
poles which should come into operation successively, and so 
attract an armature forward, is of no recent date. Multipolar 
motors are to be found in some of Wheatstone’s earliest 
patents, whilst several of Pacinotti’s motors of about 1861 to 
1865 embody the same idea. In none of these, however, was 
there any suggestion that the shifting poles should operate by 
inducing currents in the rotating part. 

The First Induction motor .—Amidst the crowd of modern 
inventions little note has been taken of the modest beginnings 
of the polyphase motor, the birth of which dates from 18T9. 
Fig. 89 illustrates the elementary motor which Mr. Walter 
Baily exhibited to the Physical Society of London on June 
28, 1879, on the occasion of his reading a paper entitled, “ A 
Mode of Producing Arago’s Rotations.” 

Down to that date the only mode of producing the Arago- 
rotations of a copper disk had been by rotating beneath it a 
steel magnet. Baily, instead of rotating any material magnet 
below the disk used a fixed electromagnet, but caused its 
magnetism to shift progressively between four successive 
poles, thus producing in the copper disk pivoted above them 
eddy-currents, which by their reaction gave the disk a 
mechanical motion in the direction of the progression of the 
poles. 

The disk in this primitive model is about 2f inches in 
diameter ; the four magnet cores are about 4 inches high, 
joined to a common yoke ; and each is wound with about 150 
turns of insulated copper wire 2*5 mm. in diameter. The 
coils are connected two and two in series, like two independent 


Early Development of the Polyphase Motor. 85 

horseshoe magnets set diagonally across one another. The 
two circuits are brought down separately to an ingenious 
revolving commutator built up of a simple arrangement of 
springs and contact strips mounted on a bit of wood, with a 



Fro. 89 .—Walter Bailey’s Polyphase Motor (1879). 

wire handle by which it is turned. On rotating it, the cur¬ 
rents from two batteries are caused to be reversed alternately 
in the two circuits, giving rise to the following successions 
of polarity in the four poles :— 

NO NN ON SN SO 

x ir Y- <- \ 

OS SS SO SN ON 

and so forth. Mr. Baily had very clear views as to how far 
this really represented a rotatory magnetic field. His own 
words are as follows : 






86 Polyphase Electric Currents . 

“ The rotation of the disk is due to that of the magnetic 
field in which it is suspended, and we should expect that if a 
similar motion of the field could be produced by any other 
means the result would be a similar motion of the disk. 

“ Possibly the rotation of the magnet may be the only 
practicable way of producing a uniform rotation of the field ; 
but it will be shown in this paper that the disk can be made 
to rotate by an intermittent rotation of the field effected by 
means of electromagnets.” The author then goes on to 
discuss the result of the increase in strength, of a pole while 
a neighboring pole of the same sign decreases in strength, 
and suggests that if a whole circle of poles were arranged 
under the disk, and successively excited in opposite pairs, the 
series of impulses all tend to make the disk move in one 
direction around the axis; adding : “ In one extreme case, 
viz. when the number of electromagnets is infinite, we have 
the case of a uniform rotation of the magnetic field, such as 
we obtain by rotating permanent magnets.” He then returns 
to the case of his actual model with two pairs of poles a a! 
and b b', and points out that if the b V , pair are arranged to 
be reversed before the a a' pair, the rotation will be in one 
direction; whilst, if the b b' pair are reversed after the a a ' 
pair the rotation will take place in the other direction. He 
goes on to show how the reversal of the direction of rotation 
may be effected either by reversing the action of the com¬ 
mutator, or by reversing the connections of one of the two 
batteries. The diagram accompanjdng the original paper 
suggests that the cores should be of laminated iron ; but those 
of the actual model are solid. In a final paragraph the author 
remarks that the effect on the disk might be much increased 
by placing four other electromagnets above the disk, each 
opposite one of the lower magnets, and connected with it so 
as to present an opposing polarity. 

The model runs exceedingly well when four dry cells are 
used to excite the electromagnets. 

On the occasion, now fifteen years ago, when the paper was 
read, and the model shown, the late Prof. Guthrie asked 
jokingly how much power it was expected that the motor 


Early Developmeiit of the Polyphase Motor . 87 

would give. To which Mr. Baily modestly replied that at 
present he could only regard it as a scientific toy. 

Researches of M. Marcel De'prez .—In 1880, M. Marcel 
Deprez brought before the Soci^te Fran 9 aise de Physique a 
paper upon the electric synchronization of rotations, in which 
artificially produced 2-phase currents were transmitted from 
a rotating commutator to a synchronous motor consisting of 
two shuttle-wound armatures set on one shaft, each one lying 
between the poles of a horseshoe magnet; one of them being 
given an angular lead of 90° relatively to the other, so that 



there could be no dead points. Fig. 90 shows how the currents 
were transmitted from the battery to the two armatures. 

This apparatus resembles that of Baily only in requiring a 
2-phase system of currents to operate it. Both will operate 
either with the artificial 2-phase currents produced by such 
commutators from a battery, or with 2-phase currents pro¬ 
duced inductively in a periodic manner. They differ, how¬ 
ever, totally in operation. Deprez’s is a mere combination 
of two ordinary motors at right angles, so as to have no 
dead-point. There is nowhere embodied in it the principle of 

























88 


Polyphase Electric Currents . 


the rotatory magnetic field. Whereas Baily’s motor possesses 
as its main feature the progressive shifting of a magnetic field 
in regular order round a centre, and develops currents by in¬ 
duction in a rotating metal mass without sliding contacts or 
commutator. 

Three years later Deprez laid down the important 
theorem which we have discussed on p. 60, as to the pro¬ 
duction of a true rotatory magnetic field by the combination 
of two alternating currents, having as their difference of phase 
a quarter period. 

Deprez’s theorem bore no fruit: it remained a geometrical 
abstraction. 

Researches of Professor Cr. Ferraris .—In 1887, several in¬ 
vestigators were independently at work. 

Professor Galileo Ferraris, 1 of Turin, had already in 1885, 
arrived at the same fundamental ideas as those of Baily and 
of Deprez. But the result was more fruitful, inasmuch as he, 
without knowing of the work of either, united both sets of 
ideas. Like Baily he proposed to produce rotation of a copper 
conductor by means of eddy-currents induced in it by a pro¬ 
gressively shifted magnetic field; and this progressively 
shifted magnetic field he proposed to generate as a true 
rotatory field by combining at right angles to one another 
two alternate currents which differed by a quarter-period 
from one another. 

In 1885, Professor Ferraris constructed the motor depicted 
in plan in Fig 91, which was not, however, publicly shown 
till 1888. It was exhibited in 1898 at the World’s Fair at 
Chicago. It consisted of two pairs of electromagnets A A 
and B B', having a common yoke made by winding iron wire 
around the exterior. Two alternate currents differing in 
phase were led into these two circuits, and the pivoted cen¬ 
tral body was observed to revolve. 

Ferraris’s first publication was in March, 1888, entitled 
Flectrodynamic rotations produced by means of alternate cur¬ 
rents . After expounding the geometric theory of the rotatory 
magnetic field, he suggested that a simple way of procuring 
the desired phase-currents would be to branch the circuit of 

1 Ferraris, “ Rotazioni elettrodynamiche,” Turin Acad., March, 1888. 


Early Development of the Polyphase Motor. 89 

ail alternate current into two parts, into one of which should 
be inserted a resistance without self-induction, into the other 
a coil of much self-induction but of small resistance. The 
two windings of the motor should be respectively introduced 
into these two branches. The difference of phase thus pro¬ 
duced would be sufficiently near to 90° to be effective. He 
expressed the opinion that in this way one might obtain all 
the effects that can be obtained by the rotation of a magnet. 
He then described the following experiments which were 
made in the autumn of 1885. 



Fig. 91.— Ferraris’ Motor (1885). Fig. 92. 


Two flat coils, one of thick wire, the other of thinner wire, 
represented diagrammatically at A A and B B of Fig. 92, were 
set at right angles to one another. Into the first was brought 
a current from the primary of a Gaulard’s transformer, and 
into the second the current from the secondary, with more or 
less non-inductive resistance. In the central space was 
suspended a small hollow closed cylinder of copper. If the 
current was turned on in one only of the two windings the 
cylinder remained immovable, but on turning on the second 
current it at once began to rotate. The sense of the rotation 
could be reversed by simply changing, with a reversing-switch. 
the connections of the second coil. The same results were 









































90 Polyphase Electric Currents . 

found to follow when a cylinder of iron was substituted for 
that of copper. A laminated iron cylinder built up of insu¬ 
lated disks also turned. Then followed suggestions for con¬ 
structing alternate current motors on this principle but of 
modified form; for, as Professor Ferraris remarked, it was 
evident that a motor thus made could not have any importance 
as a means of industrial transformation of power. He there¬ 
fore designed a larger model, having as its rotating part a 
copper cylinder weighing 10 lbs., having a length of 18 cm. 
and a diameter of 8*9 cm., borne on a horizontal shaft 1 cm. 
in diameter. It was surrounded by two sets of coils A A and 
B B at right angles to one another ,as in the Fig. 98. It was, 
however, of but small power. Fer¬ 
raris discussed the elementary theory 
of the apparatus, pointing out that 
the inductive action would be pro¬ 
portional to the slip, that is to say to 
the difference between the angular 
velocity of the magnetic field and 
that of the rotating cylinder, that the 
induced current in the rotating metal 
would also be proportional to this; and 
that the power of the motor is proportional jointly to the slip 
and to the velocity of the rotating part. Ferraris also sug¬ 
gested measuring instruments for alternate currents based on 
this principle. Lastly he succeeded in producing rotation in a 
mass of mercmy placed in a vessel in the rotatory field. In 
1894 Ferraris published a further discussion of the theory of 
these motors, which is dealt with in Chapter VIII. 

BoreVs Motor .—In 1887 M. Borel devised an alternate- 
current motor for use in a supply meter, which was brought 
out as the Borel-Paccaud meter. It was, in reality, a two- 
phase motor, in which the difference of phase was produced 
from a single alternating current by using two circuits with 
different time-constants. Upon the two sides of an iron frame 
were wound two coils A A, to give an alternating magnetic 
field in the direction from right to left. Outside the frame 
were wound two other coils B (one of them is removed from 



B B 


Fig. 93. 


Early Development of the Polyphase Motor . 91 


Fig. 94 to show the interior) tending to produce a second 
alternating field at right angles to the first. In the centre of 
the whole was pivoted an iron wheel, which was set into 
rotation by the combined rotatory field. 



Early Motors of the Helios Co. of Cologne .—In 1887 the 
Helios Co. constructed in accordance with a patent of 
Mr. Coerper, 1 some small motors, of which some were for 
monophase currents, synchronous and asynchronous, while 
another was the 8-phase motor depicted in Fig. 95. It had 
three slip-rings on the revolving part to receive a 8-phase 
current. As the motor required three leads, and as at that 
time all efforts to obtain a satisfactory working with two 
leads ”were not successful, the Helios Co. dropped the patent 
in 1890. A later patent of 1891 described a monophase 
motor with an additional winding which acts only on the 
iron of the revolving part, and is introduced only during the 
operation of starting. 

Bradley's Motors .—Amongst the early American pioneers 
of polyphase work was Charles S. Bradley, whose work dates 
from early in 1887. His U. S. patent, filed May 8th, 1887 
(No. 890,439), describes a generator with a Gramme ring, 
having four radial connectors (Fig. 96), led off at four 

1 Specification of Patent No. 9013 of 1887. See also D. R. P. 43538 of 1887, 
and 70084 of 1891. Compare Elektrotechnisclie Zeitschrift , 1893, p. 82. 



































92 


Polyphase Electric Currents. 


symmetrical points to four slip-rings. He thus obtained 
two alternate currents differing 90° in phase. The object of 
this arrangement Avas stated to be to obtain a larger output 
—which is, indeed, true, since the output of a polyphase 
machine is considerably higher than that of any other of 
equal weight. It was also stated that the machine could 
be used as a motor, though nothing was said about the 
properties of the rotatory field. Claim 9 runs as follows :— 
“ A rotary electric motor consisting of a field-magnet and 
armature and pairs of current-leading devices—such for 
instance as contact rings and brushes—the respective pairs 
being independently connected into the armature winding at 
alternating points of the same, and arranged for connection 





S 


Fig. 96. 


with two independent external circuits.” Here was, then, 
in 1887, a polyphase motor unmistakably described. In 
October 1888 (patent No. 404,465) comes an asynchronous 
motor, driven by means of directed eddy-currents in a 
stationary external mass of iron. The rotating inductor 
received 2-phase currents through four slip-rings. The whole 
principle of magnetic slip is fully explained. 

In a patent (No. 409,450), published August 20th, 1889, 
Bradley describes a similar armature tapped at three equi¬ 
distant points and connected to three slip-rings, thus con¬ 
stituting a 8-pliase system. This machine also Avas for use 
as either generator or as motor. In another patent of same 
date, Bradley indicates a method of splitting a single-phase 











Early Development of the Polyphase Motor. 93 

alternate current into two of different phases by use of his 
machines. 

Researches of Nikola Tesla .—The work done by Nikola 
Tesla between the years 188T and 1891, is of itself sufficient 
had no other workers been occupied in the same field of 
research, to have established the rotatory-field motor upon a 
solid basis. He arrived in 1886 at the firm conviction that 
some method must exist of driving an armature by currents 
induced within it, instead of driving it by currents brought 
into it (as in the ordinary electric motors), through the agency 
of metallic contacts, commutators and brushes. By October 
1887, Tesla’s work was sufficiently advanced for him to apply 
to the United States Patent Office for patents covering numer¬ 
ous points of a more or less fundamental character. Other 
applications for patents followed in November and December 
of the same year, but none were issued from the Patent Office 
until May, 1888, when a whole batch of them were granted. 

The first of these specifications set forth the general scope 
of Mr. Tesla’s ideas. He says, “ Though I have described 
various means for the purpose, they involve the same main 
principles of construction and mode of operation, which may 
be described as follows : A motor is employed in which there 
are two or more independent circuits through which alternate 
currents are passed at proper intervals, in the manner herein¬ 
after described, for the purpose of effecting a progressive 
shifting of the magnetism or the “ lines of force ” in accord¬ 
ance with the well-known theory, and a consequent action of 
the motor. It is obvious that a progressive shifting of the 
lines of force may be utilized to set up a movement or rotation 
of either element of the motor, the armature or the field- 
magnet, and that if the currents directed through the several 
circuits of the motor are in the proper direction no com¬ 
mutator will be required; but to avoid all the usual 
commuting appliances in the system I prefer to connect the 
motor circuits directly with those of a suitable alternate- 
current generator.” He then proceeds to describe by a 
diagram (Fig. 97 which is taken from Fig. 9 of the specifica¬ 
tion) how a generator is wound with two separate coils, the 


94 - 


Polyphase Electric Currents . 


free ends of which are connected to insulated contact rings on 
the shaft. From four brushes that press on the rings four wires 
are led away to the motor. This is, in fact, a simple 2-phase 
generator, inducing two-currents in quadrature. The motor 
is shown as a ring built up of core-sheets, haying wound upon 
it four coils, two of which are connected in circuit with one 
pair of wires, the other two being in the other circuit. They 
tend to co-operate in pairs to produce magnetic poles on 
diametrically opposite parts of the ring. Within the ring is 
pivoted as rotor a disk D of iron, preferably cut away at its 
sides so as to form an elongated body; and turns so as to 


MOTOR 



Fig. 97. 


convey from side to side of the ring the greatest number of 
magnetic lines. It was found that this form was not essential 
to rotation, since a circular disk of iron was also set revolving. 
This phenomenon Mr. Tesla attributed to a certain magnetic 
inertia or resistance to shifting of the magnetic lines; and 
deemed this view confirmed by the observation that a circular 
disk of steel is more effectively rotated than one of soft iron. 
In a series of eight diagrammatic figures Mr. Tesla explained 
the successive phases through which the coils of the generator 
pass during one revolution, and the corresponding and result¬ 
ing changes of magnetism produced in the ring of the motor. 

































Early Development of the Polyphase Motor. 95 

The resultant direction of the magnetic field shifts pro¬ 
gressively round (Fig. 98), dragging the iron disk with it. 

This combination amounts then to a 2-phase synchronous 
motor not operating by induced currents in the rotor, but by 
magnetic reactions, together with a suitable 2-phase generator 
for supplying the current. 

Other forms were described at the same time. A motor had 
a drum armature wound with two coils at right-angles, to which 
the currents were brought by four 
slip rings. This armature revolved 
between the two parts of an ex¬ 
terior shell of iron or steel, which 
to prevent eddy-currents (!) was 
preferably to be laminated. It 
was not wound, being magnetized 
solely by the polarity of the arma¬ 
ture. Then followed a 3-phase 
generator and motor on similar 
lines to the 2-phase generator and 
motor first described. The gene¬ 
rator had three revolving coils and 
six slip-rings. It was connected 
by six line-wires to the ring of the 
motor, which had six coils wound 
upon six inward pointing poles, 
constituting a 2-pole field with 
three phases. The rotor was as 
before a disk or cylinder of iron cut 
away on two sides to form an elongated body. The nextform 
described was a 2-phase combination, having in the generator 
a revolving magnet and two pairs of fixed armature coils, while 
the motor had as before a cut-away disk of iron as rotor, 
surrounded by two fixed coils set at right angles to one an¬ 
other. A form of motor was shown having arrangements for 
bringing the 2-phase currents to its revolving windings as 
well as to windings on a fixed external ring. It was found to 
be advantageous in the case where an external iron shell or 
fixed magnet was employed to give this a fixed magnetic 


































9 6 


Polyphase Electric Currents . 


polarity by separately exciting it with a continuous current. 
These motors were of course synchronous. Transformers for 
currents such as were used in these systems were made 
by winding a set of primary and a set of secondary wires 
upon the same ring of laminated iron, in which the mag¬ 
netism underwent a progressive shifting of polarity. In 
November came the first suggestion of a real induction motor. 
Hitherto Mr. Tesla had produced and maintained the rotation 
by the “ direct attraction ” of the magnetic elements of the 
motor. “ I have discovered,” he says, “ that advantageous 
results may be secured in this system by utilizing the shifting 
of the poles primarily to set up currents in a closed conductor 
located within the influence of the field of the motor so that 
the rotation may result from the reaction of such currents upon 
the field.” He placed within the ring that was to generate 
the rotatory magnetic field, a soft iron cylinder or disk, carry¬ 
ing two coils of insulated wire wound at right angles to one 
another, and having their respective ends joined so that each 
formed a separate closed circuit; this was placed on an axis 
mounted on bearings. In another form the rotor was formed 
of an iron core, built up of disk to prevent eddy-currents, and 
enclosed within external coils or conductors, “ applied to the 
cylinder longitudinally,” formed into one or more independent 
circuits around the core. If copper plates were thus em¬ 
ployed they were to be slotted longitudinally. This construc¬ 
tion, using induced closed circuits on the revolving part of a 
motor wound for a progressive shifting of the magnetic 
polarity, was broadly claimed. The still wider claim of the 
discovery of a new method of electrical transmission of power 
must be given in Mr. Tesla’s own words :— 

“ I am aware that it is not new to produce the rotations of 
a motor by intermittently shifting the poles of one of its 
elements. This has been done by passing through independent 
energizing coils on one of the elements, the current from a 
battery or other source of direct or continuous currents, 
reversing such current by suitable mechanical appliances, so 
that it is directed through the coils in alternately opposite 
directions. In such cases, however, the potential of the 


Early Development of the Polyphase Motor . 97 

energizing currents remains the same, their direction only 
being changed. According to my invention, however, I em¬ 
ploy true alternating currents; and my invention consists 
in the discovery of the mode or method of utilizing such 
currents. 

“ The difference between the two plans and the advantages 
of mine are obvious. By producing an alternating current, 
each impulse of which involves a rise and fall of potential, I 
reproduce in the motor the exact conditions of the generator, 
and by such currents and the consequent production of 
resultant poles, the progression of the poles will be continuous 
and not intermittent. In addition to this, the practical diffi¬ 
culty of interrupting or reversing a current of any considerable 
strength is such that none of the devices at present could be 
made to economically or practically effect the transmission of 
power by reversing in the manner described a continuous or 
direct current. In so far, then, as the plan of acting upon one 
element of the motor is concerned, my invention involves the 
use of an alternating as distinguished from a reversed current, 
or a current which, while continuous and direct, is shifted from 
coil to coil by any form of commutator, reverser, or interrup¬ 
ter. With regard to that part of the invention which consists 
in acting upon both elements of the motor simultaneously, I 
regard the use of either alternating or reversed currents as 
within the scope of the invention, although I do not consider 
the use of reversed currents of any practical importance. 

“ What I claim is— 

“ The method herein described of electrically transmitting 
power, which consists in producing a continuously-progressive 
shifting of the polarities of either or both elements (the arma¬ 
ture or field-magnet or magnets) of a motor by developing 
alternating currents in independent circuits, including the 
magnetizing-coils of either or both elements, as herein set 
forth.” 

In April 1888, Tesla finds he can use a common return in 
a 2-phase system, and so reduces the four wires to three. He 
also shows how to take off 2-phase currents from an ordinary 
continuous current dynamo, by providing it with four slip- 
7 


98 Polyphase Electric Currents . 

rings which are severally joined to four symmetrical points 
on its commutator. Passing on to generators which (like the 
well-known Thomson-Houston arc-light dynamo) have three 
coils united at a common joint, with their free ends connected 
to the segments of a commutator, Tesla shows that by con¬ 
necting each of the three ends to a separate slip-ring with 
collecting brushes, three alternating currents can be taken off. 
These will be in three symmetrical phases. He suggests that 

in this case the motor or trans¬ 
former should also be fur¬ 
nished with three energizing 
coils placed symmetrically. 

From an early period in his 
researches Tesla seems to have 
grasped the importance of 
multipolar designs in reducing 
the speed. In May, 1888, he 
already had multipolar syn¬ 
chronous motors, and later 
this feature developed. Fig. 
99 shows a design of a 4-pole 
field having four poles in 
the A circuit (alternately N 
and S poles), and four inter¬ 
mediate poles in the B circuit. In such a case the progres¬ 
sion of the field is not a uniform rotation. The field of a 
pole at A does not shift round to the next pole at B. What 
happens is that the magnetism of the A pole dies out, while 
fresh magnetism grows in the neighboring B pole. 

In April 1889, Tesla describes methods of operating two- 
phase motors from an ordinary (single-phase) alternate cur¬ 
rent, by using the device of splitting the phase, for starting 
synchronous motors; putting the two sets of coils in parallel 
with a non-inductive resistance in one branch (Fig. 100), and a 
self-inductive resistance (or choking-coil) in the other branch. 
When the motor has started these are cut out; but the motor 
continues to revolve as a synchronous motor. This device was 
not claimed generally by Tesla, and wisely, since it had already 







Early Development of the Polyphase Motor . 99 

been used by Ferraris (p. 89); but he claimed it as a means of 
starting a synchronous motor. His words are :—“ I believe I 
am the first to operate electromagnetic motors by alternating 
currents .... by producing a progressive movement or 
rotation of their poles or points of greatest magnetic attrac¬ 
tion by the alternating currents until they have reached 
a given speed, and then by the same currents producing 
a simple alternation of their poles, or, in other words, by a 
change in the order or character of the circuit connections to 
convert a motor operating on one principle to one operating 
on another for the purpose described.” None but synchron¬ 
ous motors appear to be contemplated. 



Fig. 100.-Phase-splitting Device. 


This was followed by other patents for various species of 
split-phase motors, including one illustrated in Fig. 101, in 
which there are two sets of coils to be united in parallel to 
ordinary alternate-current mains. The coils of one set were 
wound of thick wire on long iron cores, having much self- 
induction and small resistance; the others were wound on 
very short poles with wire of high resistance. The result is 
to retard the currents through the former as compared with 
the latter, and so establish a progressive shifting of polarity. 
Sundry other forms were devised between 1889 and 1891, 
when the series closed with a form of six-pole motor, in which 
the desired difference of phase was produced in one set of 





























IOO 


Polyphase Electric Currents. 


coils by the use of a condenser excited by currents in a 
secondary winding. This important series of patents passed 
into the possession of the Westinghouse Company. For 



Fig. —101.— Spljt-phase Motor. 


fuller accounts of Tesla’s work see his lecture of May, 1888, 
before the American Institute of Electrical Engineers ; also 
the volume on Tesla’s Inventions by Mr. T. C. Martin. 

Haselwander's Motors .—In the summer of 1887, Hasel- 
wander, an engineer of Offenburg (Baden), constructed a 
8-phase machine of about 10 horse-power, having a stationary 
ring-armature 40 centimetres in diameter, wound with 12 coils, 
and an internal revolving 4-pole field-magnet. It had also a 
commutator to excite its own field-magnet. It was exhibited 
in 1891 at the Frankfort Exhibition. Haselwander’s leading 
idea was as follows:—Every ordinary dynamo or motor for 
continuous currents really generates in its successive groups 
of coils alternating electromotive-forces in different phases ; 
and the commutator serves to change these polyphase currents 
into an overlapping succession of uni-directional currents. 
In the transmission of power by means of continuous currents, 
two such continuous-current machines are joined together by 
two conducting lines. The pulsating continuous current given 
off by the primary machine (or generator) is again resolved 
into its components by the commutator of the secondary 
machine (or motor), and returns to the form of a series of 











IOI 


Early Development of the Polyphase Motor. 

polyphase alternating currents. So now the idea occurred to 
the inventor to suppress the two similar but converse operations 
of first uniting and commuting, and then of commuting back 
and resolving the polyphase currents generated in the separate 
sections of the armature. Thus one arrives at polyphase 



Fig. 102.— Haselwander’s Motor (1887). 


transmission of power and suppresses the commutator and 
brushes, except so far as these may be used in an auxiliary way 
to divert a small fraction of the currents to excite the field- 
magnets. The grouping of the coils was that of a star, but 
the coils were provided with terminals which enabled the 


























102 Polyphase Electric Currents . 

individual coils in each of the three phases to be grouped 
either in series or in parallel. Each of the 12 coils had 
52 windings of 1*52 millimeter wire. A current of 24 amperes 
at 100 volts could be taken off in each phase, at 960 revolu¬ 
tions per minute. This machine is described in a lecture by 
Dr. J. Epstein, in the Elektrotechnische Anzeiger , 1891 d 
Wilson's Motor. —In a patent specification (No. 18525 of 
1888) E. Wilson describes a 2-phase motor having an arma¬ 
ture of ring or drum type, with commutator. Two-phase 
currents were supplied to both field-magnets and armature, 
the direction of rotation being controlled by the position of 
the brushes. 

Wenstrom's Motors. —The late Mr. Wenstrom in 1890 
took out a British patent (No. 5423 of 1890) for a 3-phase 
system. He describes, and gives a remarkably clear winding- 
diagram of a 3-phase generator. He proposed to join up the 
three windings in star fashion. A 3-phase transformer and a 
3-phase motor are also included in the specification. 

M. von Dolivo Dobroivolslcy's Researches. —M. von Dolivo- 
Dobrowolsky is one of the chief electricians of the Allgemeine 
Elektricitats-Gesellscliaft of Berlin. To him we owe the 
term “Drehstrom” (originally applied to a 3-phase system), 
to denote a polyphase system of currents. 

The first of Dobrowolsky’s British patent specifications 
(No. 10933 of 1889) relates to the rotors of polyphase 
machines, and refers specifically to the production by 
Ferraris of rotatory fields in which conducting bodies are 
acted upon by eddy-currents induced in them. The pro¬ 
posal was to use as rotor an iron body in which there are set 
conductors or veins of copper, bars or strips, arranged so as to 
be transverse both to the direction of rotation and to the lines 
of the field; these conductors or strips being short-circuited at 
their ends. The drawings show simple forms of short-circuited 
rotors (including a 44 squirrel-cage ”) with solid iron bodies. 

The next two patents (19554 and 19555 of 1889) relate 
to a form of polyphase generator and to a 3-phase trans- 
1 See also the official report of the Electrotechnical Exhibition at Frank¬ 
fort of 1891 (pub. 1893), p. 251; also Elektrotechnische ZeiUchrift , 1891, pp. 
540 and 609. 


Early Development of the Polyphase Motor . 103 

former. The latter had a 3-branched core; the magnetic 
circuit forming a star-combination. 

In August 1890, comes specification No. 13260 of that 
year, with the device of adding to the common junction of a 
3-phase (or w-phase) system a common return, so as to render 
the three (or more) circuits independent of one another, and 
with regulating apparatus to control the pressures in each of 
the circuits. Two 3-phase adjustable auto-transformers are 
described, one of them being for long-distance work ; and a 
combination of three separate transformers is also described. 

Specification No. 20425 of 1890 describes a laminated rotor 
wound with insulated coils; and after pointing out how, at 
starting, the reaction of the rotor currents interferes with the 
field produced by the primary currents and diminishes the 
torque, proposes the method of introducing into the rotor 
circuit resistances capable of regulation. Liquid resistances 
are shown in the drawings. 

In specification No. 3191 of 1891, Dobrowolsky shows 
polyphase transformers for changing currents of any number 
of different phases into a 3-phase system, together with 
methods of transforming 3-phase currents into a larger number 
of phases. And in No. 13503, of the same year he describes 
his method of obtaining currents of intermediate phase by 
combining mesh and star systems. For instance, he showed 
how in a 3-phase system six phases of currents could be pro¬ 
duced from the three line-wires by six coils, three of which 
were in series severally with the three lines, and the other 
three joined as shunts across the lines; all six coils being 
spaced out properly on the inductor-core. By the introduc¬ 
tion of these intermediate phases, Dobrowolsky proposed to 
make the torque (which in the absence of reactions from the 
rotor would fluctuate between certain maximum and minimum 
values in each complete period) more constant. In a large 
number of figures these various modes of concatenation of 
circuits and phases were elaborated. 

Polyphase Work at the Frankfort Exhibition , 1891. —No 
record of the development of polyphase currents would be 
complete without a reference to the Electrotechnical Exhibi- 


104 Polyphase Electric Currents . 

tion at Frankfort on the Main in the summer of 1891. Though 
nominally an International Exhibition the exhibits were 
mainly by German firms ; and the feature of greatest interest 
were the polyphase apparatus contributed by many firms. 
The official report 1 gives many illustrations of these, together 
with the tests carried out during several months by the jury 
of experts. The following notes as to the exhibits of this class 
are extracted from this report. 

Messrs. W. Lahmeyer & Co., of Frankfort, sent out from 
their model central station in the Machine-hall a 8-phase 
current at 75 volts, which worked several 3-phase motors, 
including the historic machine of Haselwander (Fig. 102, 
p. 101), a 10 horse-power synchronous motor of the ordinary 
4-pole Lahmeyer type, but provided with three slip-rings 
instead of the usual commutator, and a number of smaller 
motors. 

Messrs. Schuckert & Co. had two large 2-phase generators 
with armatures of their well-known flat-ring type, provided 
with slip-rings. One of these machines was in the Machine- 
hall and furnished power to the pumping station on the Main; 
the other, situated more than a mile away, at the Palm-garden, 
supplied power to the Distribution-hall in the Exhibition. As 
the ring-winding of these armatures was joined up in a mesh 
(Fig. 52, p. 44), it was necessary to employ two independent 
circuits with four lines in total; but by the introduction of 
transformers (compare Fig. 155, p. 179), it was possible to 
use a 3-wire system of transmission to a distance. Similar 
machines, with constantly-excited field-magnets, were used as 
motors. They ran synchronously, and with a greater output 
than if used as asynchronous motors without separate excita¬ 
tion. The 25 horse-power machine used as motor in the Ex¬ 
hibition had, indeed, an auxiliary commutator to enable it to 
excite its own magnets. The 50 horse-power motor at the 
pumping station was separately excited. The transformers 
employed were also of flat-ring form, the coils being wound 
in grooves planed out from a core built up of hoop-iron 
wound up in a close spiral, 

1 Allgemeiner Bericht uber die Internationale Elektrotechnische 
Ausstellung in Frankfurt am Main , 1891, 2 vols., published Frankfort, 1893 


Early Development of the Polyphase Motor . 105 

Messrs. Siemens & Halske showed some small 3-phase 
motors, one type having a closed-circuit rotor ; another having 
a rotor provided with a commutator into which the 3-phase 
currents weie led by three equidistant brushes after having 
traversed the three circuits of the windings on the stator. 
They also exhibited two 3-phase generators ; one resembling 
their ordinary alternator, having as armature a set of 24 
bobbins (in three series of eight bobbins each) revolving 
between two crowns of 16 alternate poles ; the other on the 
lines of their ordinary continuous-current dynamos, having a 
drum armature connected at three equidistant points of the 
winding to three slip-rings. 

The Allgemeine Elektricitats-Gesellschaft, of Berlin, had, 
in conjunction with the Oerlikon Machine Company, of Zu¬ 
rich, undertaken the striking demonstration of long distance 
transmission of power, at high voltage, from Lauffen to Frank¬ 
fort, which is further described below. This was a 3-phase 
(or so-called Drehstrom ) transmission. The 100 horse-power 
motor in the Exhibition, which received current from Lauffen 
110 miles away, was employed to pump water to supply an 
artificial waterfall. It is depicted in Fig. 104, p. 108. A 
smaller 3-phase motor 1 of about 3 horse-power, used to drive 
a small continuous-current dynamo with a load of lamps, had 
a construction the inverse of that now usual in induction 
motors. The currents were led by three slip-rings into a re¬ 
volving armature, whilst a stationary external part, consisting 
of iron core-rings furnished with closed circuit winding, con¬ 
stituted an induced field-magnet. A still smaller motor with 
induction rotor without contacts served to drive a small fan. 
Other motors exhibited at the same place by the Oerlikon 
Company, constructed from Brown’s designs, had the now 
usual construction of a fixed external armature built of core¬ 
rings pierced to receive the windings ; whilst the rotor was 
also built of pierced core-rings with a simple copper circuit of 
bars short-circuited with two end-rings like a squirrel-cage. 
One of these, of 20 horse-power, at 1200 revolutions per 
minute, weighed only 420 kilogrammes. 

1 Now in the laboratory of the Technical College, Finsbury. 


io6 


Polyphase Electric Currents . 


THE LAUFFEN-FRANKFORT TRANSMISSION. 

At Lauffen, near Heilbronn, the River Neckar has a fall 
of about 12 feet. The power had for some years been 
partially utilized for a cement factory; of the 1500 available 
horse-power about 1200 was taken up by turbines, but enough 
remained to furnish 200 or 300 horse-power, and it was pro¬ 
posed to utilize this for lighting the town of Heilbronn 6 miles 
distant. While this project was under consideration, came 
the suggestion, in the autumn of 1890, to seize the opportu¬ 
nity afforded by the Frankfort Exhibition to show what could 
be done in the way of transmitting power to a long distance at 
high voltage, and at the same time to demonstrate the ad¬ 
vantages of the Drehstrom or polyphase system. Lauffen 
is 110 miles from Frankfort. To transmit, as was proposed, 
100 horse-power through three copper wires, each only 4 
millimetres thick, and with an efficiency of at least 75 per cent., 
necessitated the employment of a pressure of no less than 
8000 volts. This tour deforce was nevertheless accomplished. 
The engineer of the line and of the Lauffen generating station 
was Mr. Oskar von Miller, of Munich. With him were asso¬ 
ciated in harmonious action two great commercial firms, the 
Allgemeine Elektricitats-Gesellschaft, of Berlin, and the 
Oerlikon Maschinen-Fabrik, of Zurich. They had the cordial 
co-operation of the Imperial German Post Office in the 
diffcult task of laying out and constructing the line. 1 The 
copper wire was lent for the purpose by the firm of Hesse, in 
Hedderheim. The two generators, designed by Mr. C. E. L. 
Brown, and constructed by the Oerlikon Company, are de¬ 
scribed on p. 27. Each was capable of furnishing three 
currents, each of 1400 amperes at about 55 volts, the frequency 
being 40 periods per second. At each end of the line 3- 
phase transformers were used: at Lauffen to raise the pres¬ 
sure to 8500 volts, at Frankfort to reduce it back to about 

1 A map of the route,together with detailed descriptions of the machinery 
and line, and of the tests made by the experts of the commission under Prof 
H. F. Weber, of Zurich, will be found in the volumes of the Official Report, 
published at Frankfort in 1893. 


Early Development of the Polyphase Motor . 107 

65 volts. These transformers (some built in Berlin, others in 
Oerlikon) were immersed, for better insulation, in oil. Their 
outward form resembled that of the Hochfelden transformers 
in Fig. 44, p. 38. The connections of both low-pressure and 
high-pressure windings were star-wise, the common junctions 
being earthed in every case. Fig. 103 gives a diagram that 
is self-explanatory. The lines were carried on about 3000 
poles at a height of about 25 feet, each pole supporting three 
porcelain insulators with internal rims for holding oil. It 
crossed territories of four governments, Wiirtemberg, Baden, 
Hesse and Prussia, following generally the route of the 
Neckar Railway, but avoiding the long tunnel through the 
Odenwald at Krahlberg, by going over the mountain. The 



total weight of copper in the lines was about sixty tons. 
The construction of the line was carried out under the direc¬ 
tion of Mr. Ebert, Telegraph Inspector of the Imperial Post 
Office, which co-operated with the Wiirtemberg Royal Post 
and Telegraph Service in this undertaking. The Post-master 
General of the German Empire, Dr. Yon Stephan, took a 
great personal interest in the work, and by his influential 
support contributed much to bring it to a successful issue. 
On August 24,1891, the line was handed over by the officials 
to the Oerlikon and Allgemeine Companies, and the following 
day lamps in the Frankfort Exhibition were lit up by the 
power from Lauffen. In the exhibition there was a 100 horse¬ 
power 3-phase motor (Fig. 104 ), designed by von Dolivo- 
Dobrowolsky, and constructed by the Allgemeine Company, 
























108 Polyphase Electric Currents . 

and other smaller motors, to which allusion has already been 
made above. This motor worked a centrifugal pump, taking 
about 60 horse-power, raising water for an artificial waterfall 



Fig. 104.—Dobrowolsky’s 100 H, P, Three-phase Motor. 





























































































Early Development of the Polyphase Motor . 109 

about 33 feet high in the grounds of the exhibition. In 
addition to these motors, there were about 1000 glow-lamps 
operated by the current so transmitted. 

Great scepticism prevailed at first as to the probable 
result of the transmission under the novel conditions of using 
such very high voltages over so long a line, and with poly¬ 
phase currents. It was anticipated by some that the efficiency 
would be greatly reduced by possible disturbances due to the 
capacity of the lines acting as condensers, or to leakage over 
the 10,000 insulators on which the line was supported. In 
private, some who were very closely connected with the enter¬ 
prise expressed their fears lest the efficiency should fall below 
50 per cent., and at one time there was some apprehension 
lest the jury would not be allowed to make full tests. How¬ 
ever, as experience was gained these fears were found to be 
empty. The elaborate tests carried out by the commission 
in the autumn months, mostly at about 8000 volts pressure, 
showed that the energy given out electrically at Frankfort 
was as much (on the average)as 74 per cent, of the energy 
given by the turbines at Lauffen to the generator. The 
various sources of loss were ascertained and carefully mea¬ 
sured, and the results of the various tests embodied in 
Professor Weber’s report. It concludes with the following 
summary:— 

1. In the Lauffen-Frankfort plant for the electric trans¬ 
mission of energy over a distance of 170 kilometres, by means 
of a system of alternating currents, with a pressure of 8500 
to 7500 volts, and bare copper conductors insulated by oil 
and porcelain, the lowest output in the tertiary circuit at 
Frankfort was 68-5 per cent., and the highest output was 
75*2 per cent., of the energy given out by the turbine at 
Lauffen. 

2. In this transmission to a distance the only cause of loss 
measurable by the instruments was that due to the resistance 
of the circuit (Joule’s effect). 

3. Theoretical considerations showed that the influence 
of capacity upon long aerial bare conductors for transmission 
of energy to a distance by alternate currents, under the 


no 


Polyphase Electric Currents . 


conditions employed, and with use of a frequency of 30 to 40 
periods per second, is of so entirely subordinate a magnitude 
that it need not be considered in designing electric trans¬ 
missions. 

4. As the expression of our experience during the fore¬ 
going measurements for the determination of the efficiency of 
the Lauffen-Frankfort transmission of energy we add, as a 
fourth result:—The electrical running with alternate currents 
of 7500 to 8500 volts in conductors of more than 100 
miles in length, insulated by means of oil, porcelain and air, 
proceeds just as regularly, safely, and as free from disturbances 
as does running with alternate currents of a few hundred 
volts’ pressure over conducting wires of a few metres’ length. 

In some further researches made later in the year by 
Dr. Kittler and Mr. W. H. Lindley, 1 extra high pressures, 
exceeding in some cases 28,000 volts, were obtained by 
putting two transformers in series at each end of the line, 
with the following summary result :—The transmission of 
power from Lauffen to Frankfort, with a high pressure of 
25,000 volts (from line to line, or at 14,000 to 15,000 volts 
between lines and earth), and with a frequency of 24 periods 
per second, gave an efficiency of about 75 per cent, with a 
load of about 180 horse-power. 

The Lauffen-Frankfort transmission was much more than 
a mere experiment. It was a daring and successful demon¬ 
stration not only of the utility of high voltages in the trans¬ 
mission of power, but of the success of polyphase currents. 
As such it marked an epoch in the commercial development 
of electricity. It evoked an extraordinary interest through¬ 
out the continent of Europe, and in Germany in particular. 
One evidence of this is to be found in the circumstance that 
early in the history of the project the German Emperor 
himself made a contribution of 10,000 marks toward the 
cost of the scheme. 

1 Official Report of the Frankfort Exhibition, ii. 451. 


Structure of Polyphase Motors . 


hi 


CHAPTER Y. 

STRUCTURE OF POLYPHASE MOTORS. 

A polyphase motor has been considered above as an 
apparatus in which a rotatory magnetic field produces Arago 
rotations in a moving mass of metal. But it may equally 
justly be regarded as a sort of revolving transformer, having 
primary and secondary circuits wound upon an iron core ; the 
latter being so designed as to permit one of the two copper 
windings to revolve. 

If the portion of the motor into .-which the polyphase 
currents are led in order to produce the rotatory field is re¬ 
garded as the primary or inductor, the other portion, whether 
revolving or fixed, must be considered as the secondary or 
induced circuit. 

In effect, the primary currents induce currents in the 
secondary windings, which are then acted upon by the 
magnetic field in which they find themselves, and are ac¬ 
cordingly driven mechanically. Regarded thus, it becomes 
evident that to produce the best effects, the induced currents, 
whether called eddy-currents or not, should be provided with 
paths or conductors which will utilize them to the greatest 
mechanical advantage. If, for example, the current might be 
led through either of two paths, one of which lay in a weak 
magnetic field where its mechanical effect in aiding the 
rotation is small, the other lying in a position where at the 
moment when the current is strongest there is a strong 
magnetic field tending powerfully to aid the rotation, then 
obviously it will be advantageous to direct the current into 
the latter of the two paths. 

Again, the primary or inductor may stand still, whilst the 
secondary or induced circuit rotates ; or the machine may be 


112 


Polyphase Electric Currents . 

designed in the inverse fashion, having a primary arranged 
to revolve while the induced or secondary part stands still, 
and by its reaction drives the primary part. The former of 
these two methods has the great advantage, that, since in all 
polyphase motors, except those of the largest sizes, the 
secondary circuit need consist of nothing more than a simple 
short-circuited winding, and therefore the machine will need 
no commutator, slip-rings, sliding contacts, or flexible con¬ 
nections—a result eminently tending to mechanical simplicity. 
The latter method of design requires that slip-rings and 
contact brushes be provided to bring the currents into the 
rotating part; but enables the resistance of the secondary 
closed winding to be readily altered—which, however, is no 
great advantage. To the latter class belong a small 3-phase 
machine Fig. 95, constructed in 1887 by the Helios Com¬ 
pany ; and one of the two motors of the Allgemeine Company 
shown at Frankfort in 1891, built from the designs of 
Dobrowolsky. Few motors are, however, now made thus. 

In those machines which have a stationary inductor, the 
magnetic field revolves rapidly, and the rotating part runs up 
to synchronism, or near to synchronism with it, the magnetism 
induced in the rotating part tending to preserve a fixed direc¬ 
tion relatively to the metal mass. In motors of the other sort, 
with revolving inductor, the inductor itself tends to revolve in 
the opposite sense to that of the magnetic field which it 
itself generates; and so tends to produce in the stationary 
secondary mass surrounding it magnetism in a fixed direc¬ 
tion. Only, however, in the case of actually attaining the 
speed of synchronism does the magnetism in the induced 
part attain to fixity of direction relatively to the mass of 
metal under induction. In all other cases the magnetism 
slowly revolves relatively to the induced masses, with a 
frequency equal to the difference between that of the im¬ 
pressed currents and the frequency of the actual motion. 

Rotor and Stator .—These considerations raise the question 
whether either part, the inductor or the induced mass, can 
be truly called an armature or a field-magnet. In ordinary 


Structure of Polyphase Motors . 113 

dynamos and alternators we know that this question is settled 
not by the accidental circumstance whether the part revolves 
or stands still, but by the criterion whether the magnetism 
preserves an invariable direction or not with respect to the 
metal mass. In the field-magnet of every dynamo, motor 
and alternator the magnetism is fixed in direction. In the 
armature part of every dynamo, motor and alternator the 
magnetism changes rapidly with respect to the metal mass : 
the armature of a motor is moreover that part which receives 
the incoming current from the line. 

Hence we may regard that part of the polyphase motor 
which receives the current as corresponding to the armature, 
whilst the other part, in which the magnetism is nearly fixed 
in direction with respect to the metal masses, corresponds to 
the field-magnet: it is, in fact, a field-magnet which is not 
magnetized by any separate currents or by any commuted 
part of the current, but is magnetized by the eddy-currents 
which are induced in it. 

However, since the workman has got the notion that the 
revolving part must be called an armature, it is quite common 
to find the rotating part of polyphase motors so described. 
Yet in reality in almost all polyphase motors—for example 
Figs. 167, 169 and 170—the true armature is the part that 
stands still and surrounds the rotating part. 

To avoid all confusion on this head we shall generally avoid 
the use of the terms armature and field-magnet in describing 
the parts of polyphase motors, and shall call the rotating part 
the rotor, and the stationary part the stator; the stator wind¬ 
ing is usually the primary, the rotor winding secondary. 

Both stator and rotor are commonly built up of soft sheet- 
iron stampings, pierced with holes to receive the windings. 
Fig. 105 shows the stampings for the 4-pole, 6-horse-power, 
2-phase motor, the full drawing of which is given in Plate I. 
It will be observed that the holes are punched extremely 
near to the external periphery of the rotor and the internal 
periphery of the stator, so that, after machining, no more than 
a mere shred of iron remains, across which little magnetic 
leakage can take place. Other forms are shown in Fig. 36 and 


Polyphase Electric Currents . 


114 


X » 







Figs. 105 . 106 .— Stator and Rotor Designed by Brown. 




























































































































































































































































































Structure of Potyphase Motors . 115 

Plate II. Fig. 106 is a section of the motor parallel to the 
shaft, showing the stampings built up. The rotor is flanked 
at each end with a stout plate of metal; in large motors bolts 
are passed from end to end at some distance from the shaft. 
The figure shows the copper rods passed through paper tubes, 
and short-circuited at their ends by wide hoops of copper, 
which present a large cooling surface. 

The above remark as to synchronism must not be taken 
to mean that the number of revolutions of the rotor tends 
to become equal to the number of periods in the frequency 
of the currents. That would be the case if the field was 
bipolar. But nearly all polyphase motors are multipolar; 
and the actual speed of rotation is reduced in inverse pro¬ 
portion to the number of pairs of poles in the revolving field. 
For example, if currents of frequency 60 per second are given 
to a motor so wound that its stator produces a revolving field 
of six alternate poles, i. e. 3 pairs of poles, the polarity will 
pass 60 times a second through one-third of the circumfer¬ 
ence ; or the 6-pole field will complete 20 revolutions in a 
second, and this the speed of the rotor will tend to raise. The 
advantage of multipolar designs is, then, the attainment of 
slow speeds without the use of gearing. 

Structure of the Rotor .—It was remarked on p. Ill that for 
the best mechanical effect the currents induced in the rotor 
ought to be led through paths which are so situated as to 
contribute best to the driving forces. 

Consider the most elementary case—that of the cylinder 
of copper situated in a rotatory field, as in Ferraris’s early 
motor, Fig. 92. The effect is equivalent to that produced by a 
pair of magnet poles placed at opposite sides of the cylinder, 
and revolving around it. Suppose the north pole to be in 
front of the cylinder (Fig. 107) and to be moving past it from 
right to left (or clockwise as viewed from above). The 
inductive action will be the same as if the pole stood still 
while the cylinder revolved from left to right. This will (by 
the principle explained on p. 5) set up electromotive-forces 
in the part which is passing under the pole in a direction 
shown by the arrows, upward; and there will be set up as 


n6 


Polyphase Electric Currents. 


the result a pair of eddy-currents as indicated in the sketch. 
Now the mechanical force which a conductor carrying a 
current experiences when in a magnetic field, is always in a 
direction at right angles both to the lines of the magnetic field 
and at right angles to the line of flow of the current. That 
portion of the copper which carries the upward current 
across the field, will be urged laterally to the left, whilst 
those parts in which the current is flowing horizontally will 
simply be urged up or down and will contribute nothing to the 
torque. On the other hand the parts of the copper in which 
the currents are flowing downwards will—if they lie in the 
same magnetic field—experience forces tending to turn in the 
other sense. Clearly, then, a better result will ensue if the 



Fig. 107. —Eddy-currents 
Induced in a Copper Cylinder. 



Fig. 108. 


downward returning currents are led into some path where 
they will return across a field of opposite polarity from that 
across which they flowed up. Then they will doubly tend to 
produce rotation. 

As a first stage to this, it will obviously be an improve¬ 
ment to make in the copper cylinder a number of parallel 
slits, which extend nearly to the ends of the cylinder as in 
Fig. 108, or to build it up of a number of parallel bars all 
joined together by a ring at each end. Dobrowolsky, who 
appears to have been the first to introduce the latter construc¬ 
tion under the name of Schluss-anJcer , seems to have thought 
that the insulation of these bars from the iron core was of 

























Structure of Polyphase Motors. 117 

little importsnce. He regarded the bars as merely veins of 
copper lying buried in a solid mass of iron. 

An iron core to the cylinder is obviously a great improve¬ 
ment over a mere copper shell or solid mass of copper, since 
it greatly improves the magnetic circuit and strengthens the 
field; thereby not only increasing the inductive action of the 
stator, but increasing also the mechanical effect of the currents 
in producing a torque. A solid cylinder of iron will of course 
serve as a rotor, as it is magnetically excellent; but the high 
specific resistance of iron prevents the flow of induced currents 
from taking place sufficiently copiously; and a solid cylinder 
of iron is improved by surrounding it with a mantle of copper, 
or by a squirrel-cage of copper bars, or (like Fig. 109) by 



Fig. 109.— Modern Short-circuited Rotor. 


imbedding rods of copper (short-circuited together at their 
ends with rings) in holes just beneath its surface. But since all 
eddy currents that circle round, as those sketched in Fig. 107, 
are less advantageous in their mechanical effect than currents 
confined to proper paths, and as they, whether mechanically 
advantageous or not, consume power and spend it in heating 
effects, it is still better, as found by Brown, to adopt a still 
more careful method of construction—namely to build up the 
iron core of thin disks or rings of soft sheet iron, to insulate 
them (lightly) from one another, and to insulate them (fully) 
from contact with the copper bars which constitute the con¬ 
ducting circuit. So we arrive at the form, Fig. 109, of rotor 
which has been so generally employed for small motors, and 









n8 Polyphase Electric Currents . 

even for quite large ones, of the squirrel-cage of copper rods 
imbedded in a laminated and insulated iron core, and pro¬ 
vided with a short-circuited ring of copper (or in some 
cases of German silver) at each end. 

But this simple form was not arrived at without experi¬ 
ment. Some hitherto unpublished researches of C. E. L. 
Brown, made early in 1890, are of great interest on this point. 
Mr. Brown had a number of rings constructed, all of the same 



Fig. 110.— Experimental Forms used by Brown. 


internal diameter, wound in different ways, but all adapted to 
receive about an equal excitation by 8-phase currents, and 
also a number of different rotors of 199 cm. external diameter 
adapted to run in any of the rings. He was thus able to 
experiment upon the performance of a large variety of combi¬ 
nations, to test their torque when allowed to run at various 
speeds, and to measure their respective outputs of power. 
Fig. 110, which is copied from the drawing used in the con- 















Structure of Polyphase Motors . 119 

struction of tliis apparatus at the Oerlikon works, shows in 
four quadrants four of these ring structures, and four of the 
experimental constructions used for the rotor. The four 
rings used were as follows ,— 

A Hole-ring , pierced with 24 holes each 18 mm. in dia¬ 
meter, through each of which passed 21 wires. B. Smooth 
ring , an ordinary plain core-ring with winding in two layers, 
there being 24 groups of coils with 19 turns in each coil. 
C. Fine-tooth ring , having 48 teeth with slots between them, 
9 wires being wound in each slot. D. Coarse-tooth ring , 
having 12 wide slots, each holding 86 windings of wire. The 
length of these ring-cores parallel to the shaft was 150 centi¬ 
metres. 

The four different rotors indicated in Fig. 110 were as 
follows :— a. A solid cylinder of wrought iron pierced with 44 
pairs of holes, b. A massive wrought-iron double-T form, like 
a Siemen’s shuttle armature, but without any windings upon 
it. <?. A laminated iron cylinder built up of core-disks 
pierced with 30 holes just within the periphery, and furnished 
with stout copper rods 10 millimetres in diameter, all short- 
circuited at the ends by two copper rings to form a squirrel- 
cage. d. A massive wrought-iron cylinder surronnded by an 
outer cylindrical mantle of copper 4 millimetres thick. Be¬ 
sides these four were six others of the same size:— e , a simple 
massive cylinder of wrought iron ; /, a massive cylinder of 
cast-iron; g, a massive cylinder of steel; h, a cylinder of 
wrought iron having four large holes bored through it (as 
indicated by the dotted circle at h in Fig. 110); /, a steel 
casting shaped as a cylinder with two parallel faces cut away; 
k, a double-T like b, but built up of laminae of sheet iron; 
and lastly, a cylinder pierced with holes like 0 , but of mas¬ 
sive wrought iron, and furnished with short-circuited copper 
conductors through the holes, but without insulation. 

Of all these various rotors the laminated doublc-T proved 
the worst—it refused to run under any load. The solid cylin¬ 
der of wrought iron was much better than that of cast iron ; 
whilst the cylinder with the copper mantle surpassed both, 
whichever ring was used externally. Brake-tests were applied, 


120 


Polyphase Electric Currents . 

as well as the test of using the motor to drive a small dynamo 
of which the output was electrically measured and controlled. 
The best form of rotor, whichever ring was employed, was 
found to be the laminated cylinder having the copper 
squirrel cage. 

Of the four rings that with smooth core was found to be 
the least effective. The fine-tooth and coarse-tooth slotted 
rings gave larger torque than the hole-wound ring, but 
both of these, especially that with coarse teeth, gave rise 
to considerable heating of all the solid rotors, and caused a 
singing noise. Using the hole-wound ring, the massive 
rotors heated less strongly, but the squirrel-cage rotor, with 
insulated conductors and laminated core, remained quite cool 
as to its iron parts, and the copper parts heated but little. 
These results decided the issue in favor of the hole-wind¬ 
ings, both for rotor and stator, a construction which has since 
abundantly justified itself. 

Doubtless other pioneers have gone through similar ex¬ 
periments. It is of some interest to compare together various 
forms of winding suggested by different inventors at different 
times. Most of the forms of rotor depicted in Fig. Ill are 
taken from patent specifications, of which the dates are 
added. 

A is Tesla’s form of 1888, with two closed coils wound 
over a laminated core at right angles to one another, and is 
suitable for a 2-pole field. B is a year and a-lialf later in 
date, and presents a winding suitable for a 4-pole field. C is 
described also for a. 4-pole field, but is in reality only suitable 
for a 2-pole or a 6-pole field, as the coils are wound across 
diameters. It is only suitable, in fact, for a field in which 
there is a travelling S-pole diametrically opposite a travelling 
N-pole. For converse reasons the form D which Tesla 
describes for use in a 2-pole field is really adapted for a 
4-pole field. E is a rational winding for a 2-pole, 6-pole, or 
10-pole field, but not for a 4-pole or an 8-pole. The form 
shown at F is a simple Gramme ring wound with a series of 
coils forming a closed circuit or series of circuits. This would 
be extremely ineffective if merely coupled up in one closed 


Structure of Polyphase Motors . 





fichus Co Four-pole Field 
4887 



Dobrowolshy Two pole Field 
4883 


Fig. 111.—Various Forms of Rotors. 

























122 Polyphase Electric Currents. 

circuit, as the induced electromotive-forces would oppose one 
another. The same defect is to be noted in the form G, which 
is that proposed by Mr. C. Coerper, of the Helios Company, 
in 1887 (see p. 91). The form H is one suggested by von 
Dolivo-Dobrowolsky in 1889. 

Winding of the Rotor .—It will be convenient here to con¬ 
tinue the consideration of the best modes of coupling up the 
conductors of the rotor, or of winding it, in case it is fur¬ 
nished with an actual winding of wires. As remarked above, 
it is obvious that the best effect will be obtained by so con¬ 
necting the conductors that the currents flowing downward 
across a field of one polarity should return upward across a 
field of the opposite polarity. In a 2-pole machine, then, the 
loops of winding should span across, or nearly across, a 
diameter ; whilst in 4-pole machines the span should be 90° 
or so, and in 6-pole machines 60° or so. This condition admits 
of many groupings of the connections, and is not, in the case 
of small machines, inconsistent with the short-circuited or 
squirrel-cage form. But there is another consideration to be 
taken into account, particularly in larger machines—namely, 
the advisability of adopting such a grouping or winding as 
will permit of the introduction, at the time of starting the 
motor, of an auxiliary resistance for the double purpose (see 
pp. 148, 197) of obtaining a larger starting torque, and of 
preventing too great a rush of current when the motor is 
switched on. 

To give definiteness to the argument, let us consider the 
case of a rotor having 24 conductors carried through 24 holes 
in the periphery of the core-disks, and placed in a rotatory 
6 -pole field. If the field is revolving right-handedly with 
respect to the rotor, and a N-pole is just passing conductor 
No. 1, inducing an upward electromotive-force in it (i. e. one 
tending to send a current toward the spectator), there will be 
equal and similar electromotive-forces in Nos. 9 and 17, and 
equal but opposite electromotive-forces in Nos. 5, 18 and 21. 
To produce the best effect, these six conductors should be 
connected together, and there are several ways of doing this. 
We will regard these six as “similars.” 

Method No. 1 .—All similars in series .—If the six con- 


Structure of Polyphase Motors. 


123 


ductors are all joined in series, with a sort of zigzag or wave¬ 
winding, they will constitute a closed circuit. In that case 
there would be four such closed circuits in the winding, Nos. 
2, 6, 10, 14, 18 and 22, constituting a similar closed circuit; 
and the others similarly. 



Method No. 2. Similars connected in diametral groups .— 
Let each be connected into a closed loop with its fellow at 
the opposite end of a diameter. This gives three independent 
closed circuits for the six similars, as in Fig. 114. Or, for the 



Fig. 113. Fig. 114. Fig. 115. 


whole rotor, 12 separate circuits. But if the electromotive- 
forces acting up on one side and* down on the other, are 
equal, there is not the slightest reason why the separate loops 
should not be connected at their crossing point, as in Fig. 
115. Applying the same argument to the rest of the con- 






























124 


Polyphase Electric Currents. 


ductors, this leads to a simple bunching of all the twenty-four 
conductors together at both ends—they will be all short-cir¬ 
cuited. 

Method No. 3. Similars connected in neighboring pairs. 
—Let each conductor be paired off in a closed circuit with its 
nearest “ similar.” The result will be, as in Fig. 116, to give 
three independent closed circuits, or twelve separate circuits 
for the whole rotor. Obviously it will make no difference 
whether No. 1 is paired with No. 5 or with No. 21. Hence 
Fig. 117, which shows them all joined together at their ends 
by hexagonal connectors, will be electrically just as effective. 
The legitimate conclusion of this construction is the squirrel- 
cage structure short-circuiting all the conductors. Methods 
Nos. 2 and 3 are electrically equivalent to one another, though 
No. 3 is obviously of greater mechanical convenience. 



Fig. Fig. 117. 


)6 i* 3 


Fig. 118. 


Meteod No. 4. Neighboring conductors grouped as similars. 
Adopting the less advantageous plan of ignoring slight differ¬ 
ences of phase, and treating neighboring conductors as though 
they were simultaneously acted upon, we may combine groups 
of neighboringconductors as though they were similars. For 
instance, in Fig. 118, we may deal with Nos. 24, 1, 2 and 3, 
along with Nos. 12, 13, 14 and 15, and combine them in 
several ^ays. We may join them into four independent closed 
circuits, No. 24 with No. 15; No. 1 with No. 14; No 2 with 
No. 13 ; and No. 3 with No. 12. Or we may put them all in 
parallel, Nos. 1, 2, 3 and 24, being bunched together and joined 
at both ends to Nos. 12, 13, 14 and 15, also all bunched 
together. Or lastly we may join them in series in one single 


































Structure of Polyphase Motors. 

closed circuit in order, and finally joining the last to the first. 
In that case the whole of the 24 conductors would constitute 
three independent groups, each consisting of eight conductors 
in series. 

Another mode of grouping, electrically equivalent to the 
preceding, is to combine Nos. 1, 2, 3 and 4, with Nos. 5, 6, 7 
and 8 as returns in a group. In this case also, if the mode of 
combination were in series, the whole of the 24 conductors 
would constitute three independent groups. 

It will be evident that in the case of the combining of 
“ similars ” in closed circuits, however many of them are 
joined in series or in parallel, the current in each conductor 
will be the same independently of the grouping, because as 
they are joined up in series of 2, 4, 6 or more, the total resist¬ 
ance and the total electromotive-force increase in the same 
proportion. From this point of view, so long as “similars” 
are being dealt with, it makes not the slightest difference to 
the action of the motor whether the grouping is in independent 
circuits, or in series, or in parallel. But when it is desired to 
provide arrangements for introducing into the rotor circuits a 
starting resistance, it then becomes obligatory to use series 
methods of combining, so as to simplify the number of slip- 
rings and brushes that must be used, to reduce the quantity 
of current that must be handled, and also to minimize the 
influence of the resistance of the contact brushes, etc., after 
the additional resistance has been cut out. 

Method No. 5 . Grouping for insertion of starting resist¬ 
ance .—It is usual in cases where starting resistances are to be 
introduced into the circuits of the rotor for the purpose of 
increasing the initial torque, to provide means for leading the 
current out of the rotor by slip-rings and contact-brushes. To 
avoid complications, it is usual to group the windings star- 
wise in three series, having a common junction, each free 
end being led to a slip-ring on the shaft. From the three 
contact-brushes wires are led off through three appropriate 
resistances (frequently a liquid resistance, such as water con¬ 
taining carbonate of soda, with carbon plates as electrodes, is 
used) to a common junction. This construction, which may 


126 


Polyphase Electric Currents . 

be observed in Plate II., is used even when the currents 
supplied to the stator are 2-phase as well as when they are 
3-phase. But, for this grouping in three series it is preferable 
that the number of conductors per pole of the revolving 
field should be divisible by three. This is not the case in the 
example just considered where we had a 24-part rotor in a 
6 -pole field. With an 18-part or 36-part rotor, this could 
be done. True, the winding can be divided into three 
symmetrical series (as in method No. 4 above), but the three 



Fig. 119. —Wound Rotor of the Oerlikon Company. 


series could not be grouped as a star unless a fourth slip-ring 
were added to provide for a common return. 

Fig. 119 illustrates a wound rotor constructed by the 
Oerlikon Company. 

One detail relating to the squirrel-cage form of construc¬ 
tion is not without importance. In all the cases where the 
number of conductors on the rotor is such as to have a 
common factor with the number of poles in the rotating field, 
there is (more particularly at starting) a tendency for the 
rotor to operate unduly as a mere transformer. Such a form 
of apparatus as Fig. 120 would form an excellent 3-phase 


127 


Structure of Polyphase Motors . 

transformer without moving, the rotatory field simply inducing 
synchronous 3-phase currents in the windings of the central 
part. Now the tendency to turn in this case would be ex¬ 
tremely small. In all induction motors something of the 
same kind would tend to occur 
if the number of conductors or 
groups of conductors on the 
rotor corresponded with those 
of the stator. To avoid this it 
is usual to design the stator and 
rotor with different numbers of 
groups or of conductors, and 
in the case where the windings 
are all short-circuited together 
this is carried so far as that the 
numbers chosen shall not even 
have a common factor. As an 
example see the 2-pliase motor of Brown, Fig. 105, p. 114, 
which has the stator pierced with 40 holes to receive the 
primary winding, and has as the rotor a squirrel-cage of 37 
bars. 

Structure of the Stator .—The winding of the stator of a 
motor is commonly of the nature of a drum-winding with the 
conductors passed through holes in the iron as previously 
shown in Figs. 37, 41 and 42, though for small motors it is 
sometimes similar to the winding of a Gramme ring as shown 
diagrammatically in Figs. 49 and 57. In considering the 
theory of a motor it is usual for the sake of simplicity to take 
a simple winding like that of Fig. 49, with the field diametri¬ 
cally across the rotor. It is well therefore to follow the con¬ 
nection between such a diagram and a multipolar drum-wound 
stator such as is commonly found in practice. Fig. 121 is a 
diagram similar to Fig. 49, with only one turn on each coil 
passed through holes in the iron. Fig. 122 shows the same 
iron wound in drum fashion, the directions of the current in 
the active conductors remaining unchanged. The dots in the 
holes indicate a current coming upwards, the cross a current 
going downwards through the plane of the paper. 



Fig. 120. 




128 


Polyphase Electric Currents. 

Now imagine the stator cut through at the line C D, and 
straightened out into an arc of much greater radius, and a 



Fig. 121. 


Fig. 122. 



number of these straightened pieces put end-on to each other. 
We should then have what is shown in Fig. 123, which in 
principle is the same as the winding of Brown’s 2-phase motor 
shown in Fig. 171. 



Fig. 123. 



C. i. s. -» z a <j s « i s a. 3. 4. 

Fig. 124. 

The wire in each coil, such as that through the holes 3 and 
6 , may go several times round before passing on to the next 


























































































Structure of Polyphase Motors . 


129 


one. For instance, the winding in the particular Brown 
motor mentioned comes up 3 and down 6, then up 3 and 
down 6 again many times, and then passes up 2, being wound 
many times again through 2 and 7 before it passes on to 3 y , 
and so on. 

This winding is shown developed in a chart, Fig. 124, with 
only two windings on each coil. 

Progression of the Field .—The way in which the magnetic 
poles progress along the face of a multipolar stator with a 
winding of this kind can be seen by reference to the Figs. 125 
to 128, in which the stator surface is drawn straight instead 
of curved. 

The holes through whichthe stator conductors pass are rep¬ 
resented by the upper row of circles, the lower row represent 
the holes for the rotor conductors (but of currents in the rotor 
no account is here taken). An air space is shown between 
the stator and rotor. To distinguish the coils belonging to 
each circuit, the holes for one circuit (which we will call circuit 
No. 1) are drawn with thicker circles than the other. In 
the clock diagram on the left of each figure the thick crank A 
shows the phase of the current in circuit No. 1 and the thinner 
crank B shows the phase in circuit No. 2. In Fig. 125 the 
current in circuit No. 1 is at its maximum and circuit 
No. 2 is carrying no current. The magnetic lines will 
circulate through the iron in paths similar to those shown by 
the arrows. The magnetomotive-force exerted by the stator 
coils at each point along the surface of the stator is shown by 
the square-cornered curve below each figure. This is arrived 
at in the following manner:—In the space between the holes 
7 0 and 2 0 there is a certain magnetomotive-force due to the 
current in the conductors 6 0 , 7 0 , 2 and 3. Its amount at 
any moment may be represented by the projection of the 
crank A on a vertical line (the current in the coils being 
proportional to this projection). We may therefore draw the 
line L M equal to the projection of A; then M N repre¬ 
sents approximately the magnetomotive-force at each point 
along the surface between the holes 7 C and 2. Between 
2 and 3 the magnetomotive-force is nil, the conductors 
9 





































Structure of Polyphase Motors. 131 

on one side neutralizing the effect of the conductors on the 
other. Between 3 and 6 the force is reversed and is re¬ 
presented by the curve PQRS below the zero line. 

In Fig. 126 the phase is advanced by ^ of a period. If 
we draw for the coils of circuit No. 1 a curve similar to that 
of the last figure, taking A a, as the magnetomotive-force and 
also a similar curve for the coils of circuit No. 2 taking B b, 
as the magnetomotive-force, then the sum of these curves is 
that shown below, Fig. 126. 

In Fig. 12T the phase is advanced another of a period 
so that the currents in the two circuits are equal. The sum 
of their magnetomotive-forces is shown by the curve in this 
figure. After another of a period the curve would be of 
irregular form again like that in Fig. 126, but is not shown 
in the figures. After a further of a period the current in 
circuit No. 1 has sunk to zero and in circuit No. 2 is a 
maximum, so that the curve (Fig. 128) is similar to that of 
Fig. 125 but is shifted forward through the space of two holes. 
At a quarter period later it is shifted on past another two 
conductors and after another half period has passed all eight 
holes and is in the position shown Fig. 125 relatively to the 
next set of coils. The poles in fact have gone through a 
complete cycle. 

Though these curves approximately represent the distri¬ 
bution of the magnetomotive-force they do not represent the 
distribution of the magnetic flux, for there can be no sudden 
changes such as are represented by the corners in the above 
curves. The natural spreading of the lines of force and the 
fact that they are moving forward cutting conductors, tend to 
wipe out the effect of the corners in the magnetomotive-force 
curve, so that the curve representing the density of the flux 
at each point will be a round even curve not unlike a sine 
curve; in fact any deviation from a sine curve would be an 
irregularity strongly opposed by currents in the conductors, 
and we may therefore, without falling into any great error, 
assume that the density of the flux follows a sine curve in 
its distribution. 

It will be noticed that the maximum ordinate in the curve 


132 


Polyphase Electric Currents . 


in Fig. 127, is greater than the maximum ordinate in Fig. 

125, the ratio being as \/ 2: 1. Thus the maximum value 
of the flux-density tends to change in value. Any change 
is however opposed by the conductors of the rotor, so that 
very little change will actually take place. 

M. von Dolivo-Dobrowolsky in 1891 gave the curve shown 
in Fig. 129, in which the effect of the two magnetizing currents 
I and II in a simple 2-phase motor are added together, giving 7 


rise to a field of varying intensity shown by the upper curve 
F F, the variation amounting to 40 per cent. In Fig. 130 are v v 
given his curves for a 3-phase motor in which the variations ' 
only amount to 14 per cent. The greater the number of 9* 
phases the less does this variation become. M. Dobrowolsky W 


7 


was then of opinion that such fluctuations of the field were 






V 


y 


disadvantageous in a motor and lessened the torque, but in 
the modern light of the monophase motor it does not seem 
that they are harmful. The fluctuations, so far as they occur 
despite the counteracting effects of conductors in the vicinity, 
will act as though there were superimposed upon a constant 
rotating field a number of stationary alternating fields having 
poles at every point where a group of conductors belonging 
to one circuit lie next to a group of conductors belonging to 
another circuit and having a frequency the same as the fre- 
quency of supply. 

Flux-density .—The maximum flux-density B permissible 
in the iron of these motors depends upon the frequency of the 
supply. The loss of energy per cycle in the iron cores owing 
to hysteresis increases disproportionately to the flux-density. 
If the latter is increased from 4000 to 8000 the loss by 





T 33 


Structure of Polyphase Motors. 


hysteresis increases nearly fourfold; the law discovered by 
Steinmetz being that the loss is proportional to the 1*6 power 
of B- At high densities the iron cores would consequently 
overheat, unless the frequency of alternations were reduced. 
Or, conversely, with low frequencies flux-densities are per¬ 
missible which cannot be used with high frequencies. Kolben 
gives the following values :— 


B = 6500 to 5500 


For 40 cycles . 
“ 50 “ 

“ 60 “ 


6000 “ 5000 
5000 “ 4500 
4500 “ 4000 
4000 “ 3500 
3500 “ 3000 


“ 80 “ 
“ 100 “ 
“ 120 “ 


In the iron between the holes the flux-density is often 
greater than is represented by these figures, and may be 
carried up to 11,500 for a frequency of 40. 

The breadth of the iron of the stator (C D in Fig. 123) 
may be a little less than one-half the polar pitch so as to 
afford an easy path for one-half of the lines from one pole 
which distribute themselves as shown in Figs. 24 and 25. 




I 34 


Polyphase Electric Currents. 


CHAPTER VI. 

ELEMENTARY THEORY OF POLYPHASE MOTORS. 

In considering the theory of polyphase motors it is proposed 
first of all to give the general relations between the speed 
of revolution of the magnetic field, the speed of the re¬ 
volving part of the machine, the resistance of the circuits, 
the torque, and efficiency of the machine. Afterwards an 
analytical method of treating the theory will be given. For 
the sake of simplicity we will take a bipolar machine, the iron 
in whose stator is of the general shape shown in Fig. 105 and 
the air space so small that magnetic leakage may be neglected. 
Suppose that a rotatory magnetic field is produced by either 
2-phase or 3-phase currents in the stator. The currents in 
the rotor (as we shall see more exactly in the next chapter) 
also produce a magnetic field, which, compounded with that 
of the stator, gives rise to a resultant rotating field. It is to 
this resultant field that the electromotive forces in the con¬ 
ductors and the torque are due. We will consider that it 
consists of a uniform flux flowing diametrically through the 
rotor and cutting the conductors of both stator and rotor as 
it revolves^ 

Let £ stand for angular speed of the rotatory magnetic 
field = 2 7T n in a bipolar machine, where n is the frequency 
of period. If the machine is multipolar having m pairs of 
poles then £ = 2 w n -f- m. 

Let w stand for the angular speed of the rotating part, or 
rotor of the machine, = 2 n w 2 , where n 2 is the actual number 
of turns per second. 

Let T be the torque between the stator and the rotor. 

Let W stand for the power (total watts) communicated by 
the stator to the rotor. 


Elementary Theory of Polyphase Motors. 135 

Let w stand for the power (useful watts) actually used 
in turning the rotor. 

il — w is the slip 1 of the rotor with respect to the field, or is 
the difference of their angular speeds. If the field has an 
angular speed £1 — a> greater than that of the rotor, it is clear 
that the inductive action on the circuits of the rotor will be 
exactly the same as if the rotor were revolved backwards 
with a speed £1 — u> while the field stood still. 

W — w is the power wasted in heating the conductors and 
iron of the rotor, since it is the difference between the total 
power supplied to the rotor and the power it utilizes. 

Now W is proportional to T and to £2 , and, therefore, by 
choosing suitable units may be written W = T £1. And w is 
proportional to T and w, and may be written w — T w. 

Hence, dividing the last equation by the preceding. 

W (D 

W = n 

From this we see that the efficiency of the rotor is the same 
as the ratio of the two speeds. The efficiency of the stator 
will be considered presently. 

Further, the rotatory field motor is simply a sort of running 
transformer, of which the stator and rotor windings constitute 
respectively the primary and secondary. Now, if u> were made 
= £1 there would be no induced currents in the rotor con¬ 
ductors, the stator would then simply act as a choking coil; 
hence, it follows that if the condition of supply of the primary 
currents is that of constant voltage, the magnetic flux through 
the machine, rotating with speed £1, will have an approximately 
constant value at all loads, just as the flux in the core of an 
ordinary transformer has. This, of course, is only true when 
the current in the stator coils is unrestricted; it is not true, 
for instance, if a resistance is put in series with the stator 
coils, or when the motor is starting without an}?- resistance in 
its rotor circuit, as will be seen hereafter. Further, if there is 

1 Some writers apply the word “ slip ” to the ratio of the two speeds, ^ 
This is conveniently distinguished by the word “slippage.” 


136 


Polyphase Electric Currents. 

very little magnetic leakage in the gap between stator and 
rotor (as is indeed the case in well-designed motors), the only 
electromotive-forces in the rotor conductors will be those 
produced by the resultant magnetic field, and therefore the 
maximum currents in them will occur when the conductors are 
in that part of the field where the flux-density is a maximum. 
And as the flux is constant at all loads (subject to the above 
conditions), it follows that the torque will be proportional to 
the currents in the rotor. But these are proportional to the 
slip £1 — oj : hence, also, it follows that T will be proportional 
to £1 — w, and may be written T = b (£1 — <y), where b is a 
constant depending on the strength of the field, the radius of 
the rotor, and the length and resistance of the conductors of 
the rotor. 

We may now write:— 

Useful watts iv == b. to (i2 — w) ; 

Total watts W — b. £1 (£2 — w) ; 

Wasted watts W — w = b. Q£1 —w). 2 

Hence we may at once apply the now well-known diagram 
of motor efficiencies, by drawing a square A B C D (Fig. 131), 

having its side A B numerically 
0 equal to 12, and cutting off a 
piece B F equal to u>. The 
aim A F H I) represents the 
* total watts supplied, the area 
AFGK, or G L C H, the 
watts utilized, and the square 
K G H D the watts wasted in 
heating the conductors of the 
rotor. The efficiency will ap- 
proach unity as F moves up 
towards A; and, as with con¬ 
tinuous-current motors, if it 
were not for the weakening of 
the field by armature reaction, the output would be a maxi¬ 
mum when u> — | il, the efficiency being then only 50 per cent. 
We shall see presently that when the motor is running at 
much below its proper speed, magnetic leakage and other 







Elementary Theory of Polyphase Motors. 137 

causes play such an important part that the torque is actually 
less than at a higher speed. Fig. 131 is, however, applicable 
to cases of normal running, and shows how these rotatory- 
field motors behave in an exactly similar manner to con¬ 
tinuous-current motors. 

In good modern rotatory-field motors the slip is only, at 
the most, about 4 per cent., except for very small sizes of 
machine, where it may be 10 per cent, at full load. 

In the above investigation no account has been taken of 
the loss due to heating in the conductors of the primary or 
stator circuit. This, like the ordinary C 2 R loss in the exciting 
circuit of any dynamo, is but a small percentage of the whole 
energy supplied, and can be readily calculated from resistance 
of the stator coils. Neither has any account been taken of 
hysteresis losses in the iron of the stator, which also have to 
he supplied, as it were, by additional excitation, but are small 
in a well-designed machine. Besides losses by hysteresis or 
by eddy-currents in the iron, the friction of the journals will 
deduct from the available power. 

2. Resultant Magnetic Flux in Motor. 

It was pointed out above, from consideration of transformer 
analogies, that the magnetic flux in the motor is of approxi¬ 
mately constant value at all normal loads. And we have 
seen (p. 131) that in the air gap between rotor and stator 
the flux-density varies approximately as a sine function 
around the periphery from point to point. Let the density 
of this flux in the direction in which it is a maximum he 
called B- This flux-density, like the flux-density in a trans¬ 
former core, is the result of the magnetizing actions of both 
the primary and the secondary windings. Kapp has given 1 
a discussion of the reaction, which may be summarized as 
follows:— 

Take a line EL to represent (Fig. 132) the maximum of 
the flux-density in the motor; in a bi-polar machine it may 
be considered as revolving clockwise around O as a centre, 

1 Gisbert Kapp, “Electric Transmission of Energy,” 1894, p. 310. 


138 


Polyphase Electric Currents . 

with an angular speed £. This field is due to the joint 
action of the impressed field excited by the primary currents 
in the stator, and of the induced field excited by the secondary 

currents in the rotor. These 
rotor currents are in phase with 
the resultant field (if there is 
no magnetic leakage), and pro¬ 
portional to it, and to the slip. 
They tend to produce a cross- 
magnetizing reaction. They 
may be represented by a length 
<?, set off along the line B- 
This current c tends to pro¬ 
duce a cross-magnetizing field 
proportional to itself. Let the 
line b at right angles to B represent this cross field. Here b— 
k c where k is a coefficient depending on the reluctance of the 
magnetic circuit and the number of windings on the rotor. 
Complete the triangle B ^ a by drawing the line a . Then a 
represents in magnitude and phase the magnetic field that 
must be impressed by the primary currents in the stator, since 
B is the resultant of a and b. The angle /? is the angle by 
which the current in the rotor lags behind the impressed field. 

Further, since the torque is proportional to both B an d c — 
that is to B an d b —the area of the triangle a B b will repre¬ 
sent the torque. 

Moreover, since c depends on the electromotive force in 
the rotor conductors, it is proportional to the slip, and to B> 
and to a constant depending inversely on the resistance R in 
the rotor circuit, we may write 

„ _ B X slip 
C -R 

or slip = — ; 
and substituting b -f- k for c, 



b R 








i39 


Elementary Theory of Polyphase Motors. 

but b -h B is tan /?, hence slip is proportional to R tan p. 
That is to say, if the slip is great the angle of lag p will be 
great. 


3. Conditions of operation. 

There are three chief stages of operation to be considered; 
and for the present we will consider the supply voltage con¬ 
stant, and the machine devoid of magnetic leakage. 

(i.) Starting .— Here co = 0, and slip = 9. Rotor currents 
enormous, primary currents also enormous. Therefore, p the 
angle of phase-difference between primary currents and 
resultant field very large. Torque enormous if no magnetic 
leakage. 

(ii.) Running at Light Road .—Here & is very nearly equal 
to 9 ; and as slip is small, rotor currents will be small, and 
their reaction small. Angle P will be small, and a will not 
be much larger than B- 

(ifi.) Running with Heavy Loads .—Here 9 - io, the slip, 
must be considerable enough to allow of the generation in the 
rotor of currents considerable enough to produce the neces¬ 
sary torque at the actual speed of rotation. 

In addition to the above, if the speed is artificially brought 
up to synchronism by supplying from without power to over¬ 
come friction, etc., there will be no rotor currents and no 
torque. If the speed is artificially increased beyond this, so 
that the rotor runs faster than its field, power will be con¬ 
sumed in driving it, and it will act as a generator, pumping 
back current into the supply network, as we shall see 
presently. 


4. Starting Torque. 

In the above we have considered a motor working 
under nominal conditions, so that the rotor currents are not 
excessive and the effect of magnetic leakage has been 
neglected. When, however, the motor is being started, the 
slip is so great that enormous currents would be generated in 


140 Polyphase Electric Currents. 

the rotor circuit if of low resistance. These currents would 
call for very large currents in the primary coils to keep up the 
magnetic flux just as in a transformer. The effect would be 
threefold. In the first place, a considerable fraction of the 
pressure of supply would be lost upon C 2 R losses in the stator 
coils. Secondly, the ampere-turns of the stator and rotor 
coils, opposing each other with very great magnetomotive- 
forces, would force a number of lines along paths which do 
not thread through both sets of coils (for example, leakage 
would appear along the air-gap), and these lines would be the 
cause of electromotive-forces in the stator and rotor coils, in 
addition to the electromotive-forces produced by the common 
resultant field, and have a choking effect upon the currents in 
these coils. Thirdly, not only is the true resultant field B 
diminished by the above causes, but the little that remains is 
out of phase with the current in the rotor circuit, so that the 
reduced instead of being increased by 
excessive slip when the rotor circuit is 
of low resistance. This is very simply 
exhibited in Mr. Kapp’s construction. 
When the slip is great, the triangle 
a b will become of the form of Fig. 133 ; 
for if slip is proportional to R tan /?, 
and R is small, tan ft must be very 
great, ft will be nearly 90°, the impressed 
field a is limited by the foregoing con¬ 
siderations, so the torque (represented 
by the area) will be very small. If 
we increase R we necessarily decrease 
tan B, making B greater and the area 
greater, and so we get a greater start¬ 
ing torque. Thus, introducing a non-inductive resistance 
into the rotor circuit at starting enables the machine to start 
with a greater torque. 


torque is very much 





Elementary Theory of Polyphase Motors . 141 


5. Relation between Torque and Slip. 


In order to get an equation for the torque in terms of the 
slip and the resistance of the rotor, we note that from Fig. 
132 it follows that 

b = a sin /?, 

and B = a cos 0. 


Now, from the equation slip = 4 X we get & = 4 * 

B k R B 

Therefore, by merely altering the scale of Fig. 132, we can 



rename the sides of the triangle as shown in Fig. 134, where 
8 stands for the slip. 

From this we see that sin 0 = — ^ 8 , and cos 0 

VR 


R 

</¥+?? * 

Therefore the torque T, which is proportioned to b X B, is 
proportional to a 2 sin 0 cos 0 ; and therefore, writing q as a 
quantity involving a 2 and constants depending on construc¬ 
tion, we have 


T = q. 


8 R 

R 2 + W s 2 


Here we are assuming that a, the impressed field, is con¬ 
stant (see p. 135). 

If we wish to see graphically what this equation means, 









142 


Polyphase Electric Currents. 


we may plot out the relation between T and s as a curve, 
assuming a definite value for R. 

Take the line O X (Fig. 135) to represent the speed of 
rotation of the magnetic field, and cut off from it a part O Q 
to represent the speed of the motor. Then the remainder, 
Q X, represents the slip. This is equivalent to plotting the 
slip backwards from X. The vertical ordinates then represent 
the values of the torque as calculated from the equation. 
For example, when Q X is taken as s; P Q is plotted to 
represent the corresponding value of T. Thus, beginning at 
X where the slip is zero, we get a curve X P t u which rises 
steeply, comes to a maximum, and dies away to the vaF'e 



O t , which is the torque at starting. The torque has a 
certain maximum value for which /9 = 45°. It will be 
noted that the steep end part of the curve is nearly 
straight, being an asymptote to a straight line, which would 
represent the relation between torque and slip if the 
magnetic field were constant and there were no magnetic 
leakage. In fact, this line corresponds to the expression 
T = b (II - (o') on p. 136. Or if in our present equation we 
consider values of s, which are small compared with R, the 

equation might be written T = q JL . At the other end of 

R 

the curve where slip is great, the curve is hollow. Here 
we may approximate by supposing that s is very great 






Elementary Theory of Polyphase Motors . 143 

compared with R, or that R 2 is small compared with s 2 ; 

R 

in which case the equation reduces to T = a —. This is the 

s 

equation to a hyperbola (also shown in dot). When the 
motor is at rest s = .Q, or 0 Q = zero, giving at O t x the 
R 

value T == vjL J Q. That is to say, at starting , the torque is 

"A 

proportional to the resistance of the rotor. If we then assign 
a higher value to R, and plot out a new set of ordinates, we 
obtain a new curve (shown in dotted line) which also starts 
at X, rises to a maximum of the same height as before, and 
then falls, but this time to t 2 . The effect, then, of introducing 
more resistance is to raise the torque at starting; but it also 
has the effect of causing the maximum torque to occur when 
the slip is greater. The motor gives out practically the same 
power as before, but runs with a greater difference of speed 
between its speed at light load and its speed at full load. 
And the efficiency at full load is diminished. If, with a 5 
per cent, slip and a 95 per cent, efficiency, we do not get a 
sufficient starting torque we can get it by introducing resist¬ 
ance, and contenting ourselves (at full load) with, say, a 10 
per cent, slip, and a 90 per cent, efficiency. And one un¬ 
derstands the reason for the modern device of constructing 
the rotor so that a resistance can be put in at starting, and 
then short-circuited as soon as the rotor has got up a fair speed. 

In the various theories of the rotatory field motor 1 the 
subject is attacked from many different points of view, but, 

1 L. Duncan, ‘Alternate Current Motors,’ Elec. World, (H.Y.), xvii. 341, 
357. 

Hutin and Leblanc, La Lumiire Electrique , xl. 373. 

Dr. J. Sahulka, ‘ Ueber Wechselstrom-Motoren mit Magnetiscliem Dreh- 
felde,’ Leipzig, 1892. 

R.-V. Picou, ‘ Les Moteurs filectriques a champ magnetique tournant,’ 
Paris, 1892, 

E. Arnold, ‘ Theorie und Berechnung der asynchronen Wechselstrom- 
Motoren’ ; and see articles by same author in Elec. World (N.Y.), 1893-4. 

G. Ferraris, * A Method for the Treatment of Rotating or Alternating 
Vectors, &c.,’ Electrician , 1894, xxxiii. 110, 129, 152, 184. 

Reber, 4 Theory of Two and Three-phase Motors,’ Amer. Inst. Elec. 
Engineers, Oct. 1894. 

Steinmetz, American Inst. Elec. Engineers, December 1894, p. 803. 


i44 


Polyphase Electric Currents. 

through whatever mathematical intricacies it has passed, the 
expression for the torque is of the general form 

s R 

T==q R 2 + k 2 s* 

The above method of deducing the formula, though in¬ 
complete in so far as it does not contain symbols for all the 
quantities concerned, perhaps has the advantage of keeping 
clearly in view the main principle, and enabling the student 
to follow the physical meaning of the expressions throughout. 
The quantity Jc, it will be remembered, is a constant, depend¬ 
ing upon the reluctance of the magnetic circuit and the num¬ 
ber of windings on the rotor. It is, in fact, the self-induction 
of one complete turn of conductor on the motor, 'the quan¬ 
tity q involves a 2 and total number of complete turns upon 
the rotor. In comparing with the formula given by other 
writers, it must be remembered that s is an angular speed, 
and is equal to 2 k (n — w 2 ) (see p. 134). 

Steinmetz gives the formula for finding the torque in 
pounds at 1 ft. radius in the form 

^ fe*g*s R 

1 ~ R 2 + jfe* s 2 

to use our own symbols; g being the ratio of the secondary 
turns to the primary turns, and 

f 550 
J 746 t : p n 

where n is the frequency, and p the number of poles. Stein- 
metz’s theory is very complete in this respect, that he takes 
into account both leakage and hysteresis, and gives an ex¬ 
pression for g, the counter-electromotive-force in the stator 
conductors, in terms of the impressed volts and of an expres¬ 
sion involving these quantities. Plotting values for torque 
at different amounts of slip he gives the curve shown in Fig. 
136, which is of the same character as that given in Fig. 135, 
only extended in both directions. If the speed of the motor 





Elementary Theory of Polypha.se Motors. 145 


is run up by mechanical means beyond synchronism, the 
torque becomes negative and the machine acts as a generator, 
giving the lower branch of the curve (see p. 42). If, on the 



contrary, the motor is turned in the sense opposite to the 
rotation of the field, the torque decreases as shown on the left 
of the figure. 

10 








146 


Polyphase Electric Currents . 


CHAPTER VII. 


ANALYTICAL THEORY OF POLYPHASE MOTORS. 


The following method of treating the theory of polyphase 
motors is a modification of that due to M. Potier. 1 Instead of 
considering the rotating field as a constant flux cutting the 
conductors of the rotor as it revolves, we may resolve it into 
two alternating fluxes in the constant directions of the axes 
X and Y (Fig. 187) at right angles to each other; then all 

motions of the rotor and the 
fluxes and currents therein 
can be referred to these com¬ 
mon axes. 

Let the line O B represent 
the direction and amount of 
the rotating magnetic flux 
(that is to say, the resultant 
of the impressed field due to 
the current of the stator and 
the field due to the currents 
in the rotor). Then x and 
y show the direction and in¬ 
tensity of its horizontal and vertical components respectively 
at any instant. 

If the field revolves at a uniform speed of £1 radians per 
second, and remains constant in intensity, then 



Fig. 137. 


x = x m sin £1 t and y = y m cos £1 t 

where x m and y m are the maximum values of the horizontal 
and vertical components, and represent^ the magnitude of the 
revolving flux. 

1 A. Potier, “ Sur les Moteurs k induit ferme sur lui-meme,” Bull, de la 
Soc. Internationale des ElectricAens, May 1894, p. 248. 





Analytical Theory of Polyphase Motors . 147 


If, however, we wish to be perfectly general, and include 
elliptically rotating fields such as are found in monophase 
motors, we will write 


x = x m sin ft t and y = y m sin (ft t + 0 ), (1) 


where x m and y m are not necessarily equal. 

We will consider the general case first. 

Suppose that there are Z conductor bars in the rotor, one 


can always consider them as — spires wound drum fashion, 

A 


each spire having a certain resistance r. 

If the rotor is revolving at a speed of w radians per second 
the angle which the plane of one of the spires makes with the 
vertical may be written (o t (see Fig. 13T). 

The flux through this spire is x cos a> t — y sin t. The 
electromotive-force in the spire will be due both to the fact 
that it is changing its inclination to the fields x and y, and to 
the fact that x and y are changing in value. 

Let us write x and y for the rate of change of x and y 
with respect to time, then we have the instantaneous electro¬ 
motive force 


e =—x o) sin m t — y u> cos <0 t + x cos oj t — y sin u> t. 
e = cos o) t (f — y oi) — sin t (y + x oj) =cr, (2) 


where c is the current in £he spire. 

In order to obtain an expression for the torque due to all 
the spires, it is necessary to integrate the expression for the 
torque due to one of the spires between the limits of half a 
revolution ; and for this purpose it is more convenient to 
signify by #, the angle which any particular spire makes with 
the axis of Y. Then the torque due to one spire == 
c (y cos a + x sin a). Filling in the value of c given above, 
and integrating between the limits a — 0 and a = tt, and 


remembering that the angle rr contains — spires so that 


2 sin 2 a = Tcos 2 a = 


Z 

T 


and 2 sin a cos a — 0 




148 Polyphase Electric Currents . 

we get the torque 

T (for the instant) = ~ |j/ (x — yw) — x (y -f- x 

Taking the general case where x — x m sin i and y = y„ 
sin (12 t + <j>) and substituting the values for x , y, x and y 
we get, after integrating between the limits O. t = 0 and 
£1 t = 2 - and then dividing by 2 w, 

the mean torque = £ A [^2 D. sin <f> — u> 0 2 „+,y 2 „)J. (3) 

This general expression for the torque is applicable to every 
form of polyphase motor with elliptical rotating fields. If the 
field revolves at a uniform speed and remains constant in 
value so that <i> = 90° and y m = x m this expression for the 
torque simplifies to 



If the stator is one of the ordinary type, such as is shown in 
Fig. 105, so that the reluctance of the magnetic circuit is 
practically independent of the direction of the field, the ex¬ 
pression for the components along X and Y of the cross 
magnetization due to the current in the rotor is very simple ; 
for, if we denote by F the flux produced normally to the 
plane of a spire by a unit current in that spire, the compo¬ 
nents x x y x of the cross field will be 

x x = — F - c cos a and y x = F 2 e sin a . 
Substituting for c its value 

~ £(# — y oj) cos a — Qy + x <o) sin aj, 

and integrating between the limits a = 0 and a = n so as to 
include all the spires, we get 

** = - ^7 (* — * •)) and = - jy {y+ x -)• (4) 

Z F 1 

For —— we will write —, so that 
4 r u 

u x x = — (x — y «) and u y x — — (y + x a>). 


Analytical Theory of Polyphase Motors . 149 

To find an expression for the components of the impressed 
field, it is only necessary to subtract the cross field from the 
resultant field ; thus if $ x and $ v be the components along the 
axes X and Y of the impressed field we have 
(p x = X — Xl and 4> y = y — y x , 
or 

u$ x = u x + x-y u>, 
u Qy = u ^ + y + x oj. 

If we know the components of the impressed field we can 
find x and y and vice versa. 

Let us now apply these formulae to the case of a simple 
motor whose rotary field has the horizontal and vertical 
components. 

x m sin 12 t and x m cos 12 t. & 

We have from equations (5) 

u x m sin 12 t +x m 12 cos £2 t—a> x m cos £2t — u$ x , 
from which we get the component of the impressed field 
along the axis of X 

x u v 

where 

a , -1 £2 — a > 

ft = tan - 1 - 

u 

Along the axis of Y it has the same value, but varies as 
the cosine instead of as the sine. 

The torque, as we have seen, p. 148, is 

-— X (12 - CD), 

4 r m 

To obtain the power yielded by the rotor, multiply by the 
angular velocity w 

P = (f2 — oj). 

4 r v 

Next consider the heat produced in the rotor. In one 
spire heat is being produced at the rate of r c 2 joules per 






150 Polyphase EleUric Currents . 

second. Filling in the value of c, and integrating as before 
for the whole of the spires, we get 

— y ™) 2 + {y + x o-) 2 J 

as the rate for the instant. 

Now taking the average of this throughout a complete 
period we find 

H, the heat produced per second, 

= i 1~ r [ol + yj (' Q2 + <" 2 ) — 4 y m a W sin (|. 

In the case of the uniformly rotating field x m = y m >, and 
sin ^ = 1, so that 

H = (D. — a,y. 

Therefore, 

P + H = x\ [ (n - «0 2 + • (fl - •) ] 

and the efficiency of the rotor 

P = 

P + H £1' 


which is the result arrived at from other considerations (see 
p. 135). 4 

In considering the loss in a 52-pole stator we will denote 
the total number of active conductors on it by Z x (so that the 
Z 

number in one coil is —*) and the total resistance of these if 

4 

joined in series by R. The difference of potential at the 
terminals of one of the circuits—for instance, that which 
produces the horizontal flux (the stator being joined up as 
shown in Fig. 49—can be found as follows:— 

We have seen that the horizontal impressed flux 


V v? + (P — - 


• x m sin (P t -J- /5), 


u 





Analytical Theory of Polyphase Motors . 151 

and this must be equal to 


Z, F 


A, 


where c x is the current in the stator coil, therefore, 

_ 4 V M 2 + (fi — «) 2 

Cl ~~z£~ « 


x m sin (H i — /?), ( tX- 


and the difference of potential at the terminals of one of the 
circuits for the instant 

R , Z, . 
ei = _ c 1 + 1 lx. 


R Z 
r 


Filling in the values of c x and x and writing A for r 
this gives us 

e x — x m £1 |j2 A sinJfi t + ^1 + 2 A ^ ~ ^ cos £1 t J ; 

If we write this in the form 

= e m sin (£1 t -j- y ), 
we find that the tan y 


'\jivn 


r 


£1 — co £1 

yrr + wrz-' 


' a — 

The lag of the current was where tan /? =-- 


therefore the difference in phase between current and electro¬ 
motive-force (j> x is such that 

, , _ u £1 

Y' ai1 ~ £1 (£2 — < 0 ) + 2 A u* + (jQ _ wf- 

The heat per second generated in the stator = R c? 

— XR02 ( 4 V— ± R Z ( /4r V Z < z)2 —ix u 2 pf — H ; 
m \zTF/ 2 z,2fAzF/ V ” 2 "r *’ 


or substituting the value for 0 W , 


N r 
t? -5 









Polyphase Electric Currents. 

summarize these results write K = -— then we 

4 r 

The torque T = K (Ct — w), 

The power P = K at (/2 — «>), 

The rotor heat H = K (il — «>) 2 , 

The stator heat = K 2 A [m 2 + (P — w ) 2 ]- 

The maximum value of the back electromotive-force of 
one circuit of a two-phase stator 

E„ = a (l + 2 A nearly. 

The maximum value of the current in the stator when the 
motor is running normally loaded, 

4 k f + (n - «o 2 _ 

Cl _ XF- u -^ 

The difference of phase is given above. 

In the above it has been assumed that the whole of the 
flux passing through the rotor cuts the stator conductors. 
This, under normal conditions of load, is very nearly true ; 
but at starting, for the reasons stated on p. 140, it is not true ; 
a large fraction of both stator and rotor fields being closed 
along independent paths. To make the theory applicable to 
all speeds and loads, the self-induction of each circuit as well 
as the mutual induction between the circuits must be taken 
into account. The expressions involving all these terms 
become so complex that they are of no practical utility even 
if the quantities involved could be determined from a given 
design. The author has therefore thought that the elementary 
theory given in Chapter VI., and the indication of a method 
of treating the subject analytically given in this chapter, will 
be more acceptable to the student than a reiteration of the 
more extended theories, reference to which will be found on 
p. 143. 


152 

To 

have 





Monophase Motors. 


153 


CHAPTER VIII. 

MONOPHASE MOTORS. 

Motors for use with a monophase—that is to say, with an 
ordinary—alternate current have the obvious advantage that 
they only need two lines instead of three or four wherewith 
to supply them with currents, and can be run from alternate- 
current lightning mains, as existing in many of our towns. 
Prior to the invention of polyphase motors, the only alternate- 
current motors in use were the ordinary alternate current 
machines (designed as generators) having separately-ex¬ 
cited magnets. These only ran in perfect synchronism, and 
were not self-starting. But as soon as the polyphase asyn¬ 
chronous motor had reached the stage of practical success, it 
became evident that monophase motors might be constructed 
on analogous lines. 

When an alternate current is passed through one group of 
coils of a polyphase motor, it produces a magnetic flux in a 
certain fixed track through the rotor. This flux rises to a 
maximum, dies down to zero, changes in sign, and rises to 
a negative maximum and so on, but it does not change in 
direction as a rotating field. Very powerful currents will be 
produced in those rotor bars which enclose this flux, but 
there will be no more tendency to turn in one direction than 
in another. Just as in a steam engine with a single cylinder, 
the forces are harmonic and rectilinear; with the crank at a 
dead point it is impossible to start without the interference of 
some outside force to upset the balance. Once give the rotor 
a good start and it will go on increasing its speed until syn¬ 
chronism is nearly reached and will exert a great torque 
The reason of this will appear from the theory of monophase 
motors presently to be considered. 


!^4 Polyphase Electric Currents . 

If we take a solenoid (Fig. 138) with a bundle of iron wire 
for a core, and pass round it an alternating current, a simple 
alternating field is produced. If in this field we suspend a 
copper ring, as shown in the figure, we find 1 that it tends to 
turn until its plane is parallel to the direction of the flux, so 
that it does not enclose any magnetic lines. It is only when 
the ring is in an oblique position that it tends to turn. If it 
be placed with its plane directly at right angles to the direc¬ 
tion of the magnetic lines, it will remain stationary ; if ever 
so little displaced to the right or left, it will turn until its plane 
is parallel to the lines. If /? be the angle between the plane of 
the ring and the direction of the magnet field (Fig. 139), the 
electromotive-force, and therefore the current induced in it by 
the alternation in strength of the field, will be proportional to 



Fig. 138. 




sin (3. Now the turning moment acting upon the ring is 
proportional to the current in it, to the strength of the field, 
and to the cosine of the angle /?. Hence it is proportional 
to the product sin (3 cos (3. The tendency to turn is zero 
both at o° and at 90°; in the former case because there is no 
current, in the latter because the current has no leverage. It 
is a maximum when /? = 45°. 

Even in this position there would be no torque if there 
was no lag of the currents in the ring ; for the phase of the 
induced E.M.F. is in quadrature with the phase-state of the 
field. When the field is of maximum strength there is no 
E.M.F., and when the E.M.F. reaches its maximum there 
would be no field. But if there is self-induction in the ring 


1 See Elihu Thomson’ “ Novel Phenomena of Alternating Currents,” Elec¬ 
trical World (N. Y.), May 28, 1887. 































Monophase Motors . 155 

causing the current to lag, tliere will be a net turning moment 
tending to diminish p. The largest torque will be obtained if 
the self-induction and resistance of the ring are such, relatively 
to the frequency, that 2rwL = r; or when the lag of current 
in the ring is 45°. 

This phenomenon may be explained by saying that the 
current induced in the ring produces a cross-field, which, being 
out of phase with, and inclined to, the field impressed by the 
primary alternate current, causes a rotary field; and this in 
its turn reacting on the conductor, a turning moment results. 

A more precise way 1 of stating what occurs is the following. 
Suppose that the ring is inclined at an angle p to the direction 
of the field impressed by the solenoid. The actual flux pass¬ 
ing through the ring will be the resultant of (1) the component 
of the impressed flux in the direction normal to the plane of 
the ring, and (2) the cross flux due to currents in the ring. 
This resultant flux will follow a 
sine law, and may be represented 
by the curve R R (Fig. 140). 

The current in the ring will be 
at right angles to this in phase, 
and may be represented by the 
curve CC, where the positive sense 
is taken in the direction of the 
arrows in Fig. 139. The cross 
field will then be represented by the curve X, and the normal 
component of the impressed field will be represented by the 
curve 11, which is obtained by subtracting the ordinates of 
X X from those of R R. It will be seen that the impressed 
field, which is of course proportional to its normal component, 
is partly in phase with the current, so that their product is, 
upon the whole, positive, and applying Fleming’s rule to 
Fig. 139, it will be seen that the torque is in the direction 
tending to lessen p. 

1 For complete analytical treatment of this subject, see G. T. Walker, 
“ Repulsion and Rotation produced by Alternating Electric Currents.” Phil . 
Trans. Royal Society , 1892, A, 279. See also J. A. Fleming, on “Electro¬ 
magnetic Repulsion,” Proc. Royal Institution , xiii. 296, March 6, 1891, and 
Journal of the Society of Arts, May 14, 1890. 





Fig 140. 



156 Polyphase Electric Currents . 

Elihu Thompson took an ordinary continuous-current 
armature placed in an alternating field, and having short- 
circuited the brushes, placed them in an oblique position with 
respect to the direction of the field. The effect was to cause 
the armature to rotate with a considerable torque. The con¬ 
ductors of the armature acted just as an obliquely placed 
ring, but with this difference, that the obliquity was continu¬ 
ously preserved by the brushes and commutator, notwith¬ 
standing that the armature turned, and thus the rotation was 
continuous (see p. 172). 

This tendency of a conductor to turn from an oblique 
position was thus utilized by him (p. 172) to get over the 
difficulty of starting a monophase motor. 

The way in which monophase motors are commonly 
started is to superimpose upon the alternating field an oblique 
field differing in phase. This is usually done by having 
additional coils on the stator fed by a current that is out of 
step with the current of the main coils, and it is necessary to 
have some device which will cause a difference in the phase of 
the currrents of the two branches. This operation of splitting 
the phase may be performed in many ways. We have seen 
(p. 14) that in circuits possessing resistance and self-in¬ 
duction the tangent of the angle of lag of the current 

behind the electromotive-force is equal to If, therefore, 

R 

we have a comparatively large self-induction in one branch of 
the circuit, and comparatively large resistance in the other, 
the phases of the currents will differ by nearly 90°. This 
difference in the self-induction of the branches may be caused 
either by the difference in the number of turns of wire in the 
coils on the stator and the arrangement of the iron around 
them, as in the case of Tesla’s motor (Fig. 101), or it may be 
caused by putting in series with one of the branches a coil of 
iron on an iron core. A non-inductive resistance may be 
introduced into the other branch. 

A difference in phase can also be produced by giving 
one of the branches capacity by means of a condenser, 
capacity having the effect of giving the current a lead. The 


Monophase Motors. 157 

kind of condenser usually employed for this purpose is an 
electrolytic condenser, consisting of a number of iron plates 
with a solution of carbonate of soda between them. 

There are also many ways of producing a difference of 
phase by means of special transformers. These are con¬ 
sidered under the head of phase-transformation, Chapter IX. 

A simple single-phase motor with closed-coil rotor was 
described in a specification of patent filed in the English 
Patent Office in November 1892 (No. 20,505), being a 
communication from the Oerlikon Machine Company of 
Ziirich. The cause of the torque after the motor is 
started is there given in these words:—“ On rotary motion 
being imparted to the machine in any suitable manner, 
currents will be induced in those conductors of the armature 
which are approaching one pole of the exciting coils and 
moving away from the opposite neighboring pole, these 
currents being less strongly re¬ 
pelled by the first pole than by 
the second pole because, in 
consequence of the rotation, a 
given conductor will assume a 
phase which, in the position of 
rest, would belong to a con¬ 
ductor located further back.” 

A diagrammatic view of a two- 
pole motor is shown in Fig. 141. 

The windings of the stator are 
reversed so as to produce con¬ 
sequent poles at the top and 
bottom. This specification de¬ 
scribes a method of starting the 
motor by means of an addi¬ 
tional winding on the stator, carrying a current differing from 
the main current in phase in the manner described on p. 201. 

In specification of patent No. 23,902, filed by Mr. C. E. L. 
Brown in December 1892, some monophase induction-motors 
are described 1 with rotors of the squirrel-cage type. 

1 See also Elektrotechnische Zeitschrift, xi. 81, Feb. 17, 1893; Industries , 

xiv. 89. 











158 Polyphase Electric Currents. 

Since this date many monophase motors have been con¬ 
structed by both these firms ; the main differences consisting 
in the methods adopted in the starting-gear, and in the use of 
toothed core-rings as against core-rings pierced with holes. 
The dispute as to priority 1 which arose between these two 


N 



Fig. 142. 


firms in 1898 does not concern us. It appears to have been 
closed by the letter of Mr. Brown in the Elektrotechnisclie 
Zeitschrift of July 14th, 1893. 

A closely-kindred form of motor was described in May 
1891 by the Helios Co. It is depicted in Fig. 142. 

Theory of the Monophase Motor. 

The difficulty in following the action of a monophase 
alternate-current motor, lies in the fact that while there is 
passing through the rotor an impressed alternating field of a 
certain frequency, inducing currents with their opposing fields, 
there is at the same time a turning of the rotor causing the 
phenomena of currents and magnetic fields at another fre¬ 
quency. Any theory which comprises all these things, and 
takes account of the magnitude and phase of each, necessarily 
contains a complex grouping of symbols, whose physical 

1 Elektrotechnische Zeitschrift , xi. 81,178, 283, 285,411,1893; Industries , 
xiv. 89, 327, 425, 522, 1893. 2 D. R. Patent 70084. 


Monophase Motors . 


159 


meaning is not easily grasped, while a theory which for the 
sake of simplicity neglects one or more of these things is too 
incomplete to be satisfying. 

It is proposed here to give in the first place a comprehen¬ 
sive analytical theory as given by M. De Bast, 1 secondly the 
graphic method which is due to Professor Ferraris, 2 and 
thirdly to translate these into a mental picture of what act¬ 
ually goes on in the rotor. 

Assume in the first place that a two-pole motor is started, 
and running at a constant speed of m revolutions per second, 
and that it is being supplied with an unvarying alternate 
current which follows a simple sine law with a frequency of 
n periods per second; then the flux-density B of the field 
impressed by the stator coils at any instant is 

B = Bo sin 

B 0 representing the maximum flux density reached in each 
period, and n assumed constant. If A is the area enclosed by 
a conductor embracing the rotor about a diameter which 
makes an angle a with the plane normal to the direction of 
the impressed field, the total magnetic flux 

|SJ = A cos a Bo sin 2 n n t, 

the flux-density being assumed to be uniform. 

As the rotor turns m revolutions per second, 

a = 2 7T m t. 


The E.M.F. in the conductor is 


E = — 


d N 

d t 


= — A Bo [ — 2:rrasin27 rw£. sin + 

cos 2 7r m t cos 2 n n £] 

A B 

= — ^ ■ - [2 7T (n + m) cos 2 * (n + m) t + 2 n (n — m) 

cos 2 7T (n — m) £]. 


1 De Bast, Bull, de VAssoc, des Ingenieurs Electriciens , Aug. 1893. 

2 G. Ferraris, “A Method for the Treatment of Rotating or Alternating 
Vectors, etc.” The Electrician, xxxiii, 110, 129, 152 and 384. 



160 Polyphase Electric Currents . 

Thus the electromotive-force is the sum of two simple 
harmonic electromotive-forces of the frequencies (n + ni) and 
(n — rri). 

If we represent the resistance of the conductor by r, and 
its coefficient of self-induction by L, the impedances I x and I 2 
to the two electromotive-forces respectively will be 

11 = V r 2 + 4 - 2 (n + m) 2 L 2 , 

1 2 = r 2 + 4 - 2 (n — rri) 2 L 2 . 

The instantaneous value of the current in the conductor 
will be 

C = — p 71 + m ) cos | 2 7 T (?l + ni) t — (J)\ | 

-f- r ^ cos | 2 7 r (71 — w) £ — fa | J, 

the angles of lag being fa and fa, of which 

cos fa = -, 
tl 

a r 
cos fa = -. 

*2 

The potential energy of the conductor is 

W = — CN = — C A B 0 cos a sin 2 n n t, 

and in moving through the small angle da the work done is 
(neglecting the sign) 

d W = C A Bo sin 2 7 x n t sin a da. 

Substituting the value for C given above, and 2 7 t m dt for da, 
we get 

n ttt A 2 B 2 o r2 tt (n + rri) ( 0 , N , ) 
dW = —- 1 cos | 2 7 T (n + ni) t — fa l 

+ cos j 2 .(»_«) t - * } ] 

X [2 tt m sin 2 tt n t sin 2 tt m £] df. 










Monophase Motors . 


161 


Integrating this between the limits t = 1 and t = 0, we 
get the work per second, or, in other words, the mean power 
for one conductor. 

n 2 7r m A 2 B 2 w (w — m) 2 7r(w+m) 1 

p = -g-0 i COS * J 

_ 2 7r m r A 2 ^ (w— m) 2 tt (w + m)~| 

"“8 L I? I? J * 

The total mean power is obtained by multiplying by the 
number of conductors Z, and the torque is obtained by 
dividing the total mean power by the number of radians per 
second = 2 iz m. 

v ZP 

Torque = - - ; 

2 7T m 


therefore we obtain as the final expression 1 the following 
formula: 


Toraue _ r z A 2 B 2 * f (n — m) 
lorque 4 Lr 2 + 4 ^ 0 — m) 2 L 2 


__ (rc + m) ~| 

r 2 + 4 7T 2 (n + m) 2 L 2 J 

Professor Ferraris has given 2 a method of treating the 
subject in which the alternating magnetic field is regarded as 
being resolved into two magnetic fields rotating in opposite 
directions. It is a familiar point in mechanism that any 
simple harmonic rectilinear motion may be resolved into two 
equal circular motions in opposite directions. Fig. 143 illus¬ 
trates one way of doing this, the mechanism being well known 
to engineers. The amplitude of the original motion is equal 
to the diameter of each of the circular motions. Ferraris 
deals, however, with the problems of the alternating magnetic 

1 Compare Hutin and Leblanc, La Lumiere Electrique , xl. 418 (1891). 

2 Galileo Ferraris, “A Method for the Treatment of Rotating or Alter¬ 
nating Vectors, with an Application to Alternate-current Motors.” The 
Electrician, xxxiii, 110, 129, 152, 184 (1894). 












i 62 


Polyphase Electric Currents . 


field quite generally, applying the geometrical notion of 
rotating vectors. 

If we represent by the vector b x (Fig. 144) which rotates 
clockwise uniformly about O, the magnitude and direction of 
a rotating magnetic field, and by b 2 the magnitude and direc¬ 
tion of another field of the same strength rotating in the 
opposite sense with the same frequency n , it will be seen that 
the direction of the resultant field is always along the line B, 
and the magnitude of the resultant field will alternate between 
the values -f- 2 b and — 2 b following a sine function of the 
time, so that we may write B = 2 b sin 2 n n t. 



y 

Fig. 143. 


Fig. 144. 


Conversely, if we have an alternating field following the 
law B 0 sin 2 w n t as in a monophase motor, we may resolve 
it into two oppositely rotating fields of the same frequency w, 
and consider the effect of each field separately upon the rotor. 

If the rotor turns clockwise with a frequency m, the fre¬ 
quency of rotation of the clockwise field with respect to the 
rotor will be n — m, and the frequency of rotation of the 
counter-clockwise field with respect to the rotor will be 
n + m. 

Each field may be considered as generating currents in 
the rotor, and the torque due to such currents flowing through 
conductors in the field may be ascertained by the formulae 
employed in the case of rotary field motors. 







Monophase Motors. 


163 


It was found above (see p. 144) that a field rotating with 
a speed s relatively to the rotor produced a torque 

rp _ rs 

~ 2 r 2 +4^ 2 L 2 * 2 ' 


The torque produced by the two oppositely rotating fields 
will be 

Torque =qr\ _!L=*__ W + CT 1 

Lr 2 -p 4 7T 2 L 2 (w — ra)”*" r 2 + 4 tt 2 L 2 (n + ra ) 2 J 

which is the same as the expression deduced above (p. 161), 
where 




Z A 2 B 2 tt 
4 


It is not necessary to consider the torque exerted by rea¬ 
son of the fact that the currents due to one rotating field flow 
in conductors that are immersed in the oppositely rotating 
field, because the frequency of these currents differs by 2 m 
from the frequency of the opposite field, and consequently 
this torque is rapidly reversing in direction. 



In order to find the torque due to the field rotating clock¬ 
wise with the frequency n - m, we draw the curve OPQW 
(Fig. 145) (see p. 142 where the curve is reversed) showing 
the relation between slip and torque obtained by the formulae. 

rp _ V S 

^r 2 + 4 t^L 2 # 2 # 

Let O Q, represent the speed of rotation of field of fre¬ 
quency n; then measuring backwards from Q a distance Q 

















164 Polyphase Electric Currents. 

P i —m (= speed of rotor) we get the abscissa OP^w- 
m, and the ordinate P y P represents the torque in question. 

To find the torque due to the counter-clockwise rotating 
field, we measure off forwards from Q y the distance Q y U y = 
m and get O U y = n -f- m, then U U y represents the torque 
due to a slip n + m. This being in the opposite sense to the 
torque P P y we can cut off from P P y a part P P yy = U U yy 
and obtain P yy P y which represents the actual torque on the 
rotor. 

For convenience in deducting the torques due to counter¬ 
clockwise field we may draw Q W y symmetrical with Q W, 
and then deduct the intercepted parts such as U yy P y from the 
ordinates such as P P y . Doing this for all the ordinates 
between O and Q y we obtain the new curve T P yy Q y , the 
ordinates of which represent the actual torque for various 
values of m. 

When m — O, that is to say, when the rotor is stationary, 
the two opposite torques balance one another; as m is in¬ 
creased the torque rises to a maximum, and then falls to 
zero before m is quite as great as n, and further increase in 
m produces an opposing torque. 

This argument assumes that B 0 remains fixed, which is 
only true so long as the motor is supplied with the same 
current. The curve cannot therefore be taken as the true 
characteristic of the monophase motor supplied at constant 
voltage, but is useful as a simple indication of its general 
behavior. When load is thrown on to the motor its speed 
decreases a little, more current flows through the stator, and 
the impressed field is correspondingly increased, so that the 
quantity denoted by q is by no means a constant quantity, 
but increases with the load. The theory given here merely 
explains how the alternating flux is capable of producing 
rotation. 

In order to get a mental picture of what is going on in 
the rotor, let us apply the construction given on p. 138, for 
finding the direction of the resultant field and current to the 
case of the two oppositely rotating vectors. In Fig. 146a let 
O P represent by its length and direction the magnitude and 
direction of one (b x in Fig. 144) of the rotating magnetic fields 


Monophase Motors. 


165 

which together make up the alternating field B 0 sin 2 7 x nt. 
Suppose that the rotor is revolving clockwise, making m 
revolutions per second, and that O P is revolving in the same 
direction at a slightly faster speed (n revolutions per second). 
As O P cuts across the conductors of the rotor at a speed of 
(n - m) revolutions per second, it will generate currents whose 
intensity will vary at different points around the circumference 
of the rotor very nearly according to a sine law. This current, 
whose maximum intensity we will denote by Ci, will produce 
a cross magnetic field at right angles to the direction of its 
flow, whose intensity may be denoted by X x . This field, com¬ 
pounded with the impressed field, gives the resultant field, 
and we may find the direction of all three by setting off O A, 




making the angle fa (which is known, see below) with O P, 
and dropping the perpendicular P A upon it, than O A indi¬ 
cates the resultant field B v and P A indicates the cross-field X, 
in direction and magnitude. The angle fa is known because 
the ratio between the cross-field to the resultant field is known 
from considerations of the speed n - m, the resistance R, and 
the magnetic reluctance of the path, and this gives tan fa, 
(see p. 138). For instance, if the cross-flux is equal to k C x , 
then as Ci is equal to 

Bj 2 7T (n - m), 

R 

tan A= 2 »("-”)* . 

K 

fa at full load ought to be a little greater than 45°. We can 
go through the same construction with regard to O P^, Fig. 





i66 


Polyphase Electric Currents . 


1465, which represents the other rotating field (5 2 , in Fig. 
144) ; but this time, as 


tan 0 ! = 


2 7 T (n + m') k 


R 


it is about 40 times as great as tan <j> r because m only 
differs from n by about 5 per cent. 

$2 is therefore very nearly a right angle, and B 2 about one- 
twentieth the magnitude of B ; . It will be seen that the 
area of the triangle P O A is much greater than the triangle 
P' O' A', which, according to the argument on p. 188, tells 
us that the torque clockwise is much greater than the torque 
counter-clockwise. 

In order to indicate the directions of the current C x and 
C 2 , the following convention may be employed. Suppose the 
rotor bars to be short-circuited at each end by a copper disk 
extending over the whole of the end of the rotor. A uniformly 
distributed current flowing across the disk, parallel to any 
diameter, would produce a sine distribution of current in the 
rotor bars, which bring the current at one side and take it 
away at the other, the maximum intensity being in the two 
bars joined by the diameter which is parallel to the direction 
of the current. We may, therefore, in a clock diagram, indi¬ 
cate the direction and magnitude of such a current across the 
end of the rotor, by a line drawn from the centre, whose length 
is proportional to the maximum value of the current in the 
rotor bars, and this method is applicable to motors in which 
no such copper disk exists, so long as we understand the dis¬ 
tribution of current which it is intended to indicate. In Figs. 
146a and 1465, the dotted lines C x and C 2 represent in this 
way the distribution of the current at any moment. They are 
drawn in a line with B x and B 2 , the current being always in 
phase with the resultant magnetism, and they are made equal 
to Xi and X 2 respectively, those lines being proportional to 
the two currents. The arrowheads show the sense which the 
reader may ascertain by Fleming’s rule, noting that the 
arrowheads on the lines indicating magnetic flux point in the 
direction in which a N-pole would move. 

Having ascertained the direction and amount of the resul- 




Monophase Motors . 


167 

tant fields and currents due to the oppositely rotating vectors 
O P and O P\ in Figs. 146a and 1465, let us place one figure over 
the other and recombine them so as to obtain one field and 
one current. For this purpose the circle may be divided into 
a number of equal parts, say 16, which represent fractions of 
the period of one cycle. At the position 1 we have O P coin¬ 
ciding with O P', their sum being a vector of double the length 
representing the maximum value of the impressed field shown 
by the line 0 1 in Fig. 147. 



If we now add the vectors B t and B 2 , taking note of their 
sense we get the vector o 1 ', shown in Fig. 147, and adding Cj 
and C 2 we get the vector o 1 ". Then (reverting to Figs. 116a 
and 1465) move P and P' to the position 2, triangles P O A and 
P' O' A' being correspondingly slewed round. The addition 
of OP and OP!, B x and B 2 ,andC 1 andC 2 will now give the 
vectors 0 2, 0 2' and 0 2" respectively ; and so as we go round 
the circles in Figs. 146a and 1465 we shall get the various points 
1 2 8 4, etc., 1' 2' 8' 4', etc., and 1" 2" 3" 4", etc. in Fig. 147, 
through which we can draw the line and the ellipses shown. 

The two ellipses show at a glance what occurs in the 
rotor during each alternation. That numbered 1' 2' 3' etc., 
which really differs very little from a circle (its eccentricity 



168 Polyphase Electric Currents. 

being exaggerated in the figure to show how it is tilted), 
shows that there is a rotating magnetic field of slightly varying 
intensity which has the same frequency as the impressed field 
(given by the line 12 8 etc.), the latter being wiped out, or 
rather transformed into a rotary field, by the currents in the 
rotor. The sense of rotation is the same as that of the rotor. 
The other ellipse (numbered 1" 2" 3" etc.) shows that there is 
a rotary current which varies in value between very great 
limits. At the moment 1" it is just past its maximum, and is 
flowing from right to left across the end of the rotor upon 
which we are looking, at the instant 4" it is near its minimum 
value and is flowing downwards. At 8" it is very great and 
flows from left to right. It will be seen that it rotates in the 
opposite sense to the rotor and the field. To see how such a 
current and rotary field can produce a torque, we must see, in 
the first place, the relation of their phases. When the current 
is at its maximum near the instant 16" the field is in phase 
with it—that is to say, both are represented by lines in the 
same direction, with the arrowheads pointing the same way. 
This produces a great torque in the sense of the rotor 
motion. At the instants 1" and 2" the current is diminish¬ 
ing and getting out of phase with the field, but the torque 
remains positive. As soon as the angle between the two 
becomes greater than a right angle the torque becomes 
negative, but by that time the current has become small and 
the angle changes very rapidly, so that it is only during the 
instants 3" 4" and 5" that there is a small negative torque; 
during the instants 6" 7" 8" 9" and 10" the torque is positive 
again, and is very great at 8". During the period of one 
alternation the torque is twice positive and twice negative, 
but the positive torque greatly exceeds the negative, and the 
interval of time occupied by it is greater. 

It may not at first sight be apparent how a rotating field 
which varies so little in value can produce a current in the 
rotor of such great eccentricity as that shown in the ellipse. 
It must be remembered, however, that the speed of the field 
relatively to the conductors is only (n — m), while the little 
variation which takes place in the value of the rotatory field 
has a frequency of n periods per second. 


Monophase Motors . 169 

The inclination of the major axis of the ellipse 1' 2' 3' etc. 
to the direction of the impressed field increases as the speed 
of the motor increases. The angle between the two is i 

(02 - 0l)- 

The counter electromotive-force in the stator conductors 
is produced by the rotation of the resultant field we have 
been considering. Its phase is therefore shown by the posi¬ 
tion of the vector 01', 02', 03', etc., which we have seen is 
practically the radius of a circle. The counter electromotive- 
force is at its instantaneous maximum value when this vector 
is at right angles to the central line which represents the 
direction of the impressed alternating flux. The current in 
the stator coil is at a maximum at the instant 1, because the 
impressed flux is then greatest. We see, therefore, that the 
inclination of the vector 01' at this instant, or, in other words, 
the angle which it has passed through since it was perpendi¬ 
cular to the central line, gives the lag of the current in the 
stator coils behind the counter electromotive-force. For 
instance, suppose that the motor is running nearly syn¬ 
chronously, will be almost nothing, so that B 2 may be taken 
equal to and in phase with b v B, 2 on the other hand, is 
practically wiped out altogether. At the instant 1, when the 
current is at its maximum, the angle which B 1 has passed 
through since it was at right angles to the central line is about 
90°. This is the angle of lag of the current behind the 
E.M.F. As load is put upon the motor (f> 1 increases, and the 
angle of lag decreases. It must not be supposed, however, 
that Bj decreases, as it would seem to do in our figure. We 
must increase the size of our figure so as to keep the vector 
representing the resultant magnetism nearly constant. 1 It 
would thus be possible for any given motor to go through the 
construction for different amounts of slip, and plot out the 
characteristic from the differences of the areas of the tri¬ 
angles A O P and A' O' P'. 

1 The resultant magnetism is proportional to the counter E.M.F., which 
within practical working limits does not alter 2 per cent. For the exact 
relation between impressed E.M.F. and counter E.M.F. see Steinmetz, Amer. 
Inst. Elec. Engineers , Dec. 1894, p. 803. 


1JO 


Polyphase Electric Currents . 


CHAPTER IX. 

MISCELLANEOUS ALTERNATE-CURRENT MOTORS. 

Alternate-current motors may be classified as follows :— 

A. Single-phase Synchronous .—Ordinary alternate-current 

machines, in fact, used as motors. They are not 
self-starting. 

B. Polyphase Synchronous. —Mentioned below. 

C. Polyphase Asynchronous .—The main topics of this work. 

D. Single-phase Asynchronous .—The monophase motors 

already considered, and which require a starting-gear 
of some sort to split the phase. 

E. Series-wound Laminated Motors .—For small sizes any 

form of continuous-current motor with ordinary 
commutator and brushes, provided the field-magnet 
is thoroughly laminated. They are not altogether 
satisfactory, as their self-induction is generally too 
great. 

Synchronous Polyphase Motors .—A polyphase system of 
distribution, while giving great facility in the use of self¬ 
starting motors, does not sacrifice the possibility of installing 
synchronous motors incases where perfect uniformity of speed 
is desired. A synchronous motor for a polyphase system 
may consist of an ordinary alternator placed across two of the 
mains ; but preferably it is identical in construction to the 
polyphase generators described in Chapter I., and connected 
to all the lines. It differs from an asynchronous motor mainly 
in the fact that instead of a rotor it has a field magnet 
separately excited by means of a continuous current ; and as 
the poles always keep the same position relatively to the iron 
of the magnet when once they are run up to the speed of the 


Miscellaneous Alternate-Current Motors. 171 

revolving poles of tlie armature, the North and South poles 
take hold of each other and the magnet is dragged round in 
perfect synchronism. For the principles which govern syn¬ 
chronous running the reader is referred to the author’s treatise 
on Dynamo-Electric Machinery, and to other works 1 on the 
subject. The ordinary single-phase synchronous motor must 
be run up to speed by some independent source of power; 
but in a polyphase system the rotatory field acting upon eddy- 
currents in the broad unlaminated poles of field-magnets is 
sufficient to start the motor. It is thus possible to so far 
combine the principle of a polyphase asynchronous motor 
with a truly synchronous motor, that it shall be capable of 
starting itself, and after running up to speed, will keep its 
speed at all loads as constant as the periodicity of the supply. 
It is to be noted that while a polyphase generator will always 
act as a synchronous motor, it is not necessarily self-starting. 
Its design should facilitate the generation of currents in the 
polar projections if it is intended to be self-starting. A very 
good instance of an installation of synchronous motors of this 
kind is at the Ponemah Cotton Mills, Taftville, Conn., U.S.A. 2 
Six hundred horse-power is transmitted from a mill 3 miles 
distant, where water power is available, at a pressure of 2500 
volts. The system is a 3-phase one. The motors are the 
same in construction as the generators, and while being able 
to start themselves, run under load with perfect synchronism. 
The efficiency of the complete transmission from the power 

1 Dr. J. Hopkinson, “On the Theory of Alternating Currents, particu¬ 
larly in reference to Two Alternate-Current Machines connected to the same 
Circuit.” Journ. Soc. Tele. Engineers, vol. xiii. p. 496, 1884. 

W. M. Mordey, “On Parallel Working, with Special Reference to Long 
Lines,” Inst, of Elec. Engineers , xxiii. 260, 1894. 

Blondel, “Couplageset Synchronisation des Alternateurs,” La Lumiere 
Elec., xlv. 351, 1892. 

Steinmetz, “Theory of a Synchronous Motor,” Amer. Inst. Elec. Engi¬ 
neers, Oct. 17, 1894. 

Picou “Transmission de Force par Moteurs Alternatifs Synchrones,” 
Soc. Internationale des Electriciens, Feb. 1895. 

Bedell and Ryan, “ Action of a Single-Phase Synchronous Motor,” 
Journ. Franklin Inst., March 1895. 

Rhodes, “ Theory of the Synchronous Motor,” Proc. Physical Society , 
1895. 

2 Elec. Rev. (N. Y.) xxiv. p. 210, May 2, 1894. 


172 


Polyphase Electric Currents . 

applied to the dynamo pulley to that delivered to the motor 
pulley is reported to be 80 per cent, 

A number of alternate-current motors have been devised 
which do not come under any one of the preceding classes, 
and yet are hardly susceptible of classification. 

Elihu Thomson's Motor .—In the course of his observations 
on the effects of alternate currents, 1 in 1886-7, Elihu Thomson 
observed that a copper ring placed in an alternating magnetic 
field tends either to move out of the field or to return so as 
to set itself edgeways to the magnetic lines. It follows that 
if an ordinary armature (say drum-wound) is placed in an 
alternating field, and the brushes are given an angular lead 
in either direction and then short-circuited together, the 
armature will turn, and yield considerable power. When once 
so set turning, the armature will continue to rotate, even if 
the brushes are disconnected or thrown off. Following up 
this plan, he then constructed motors in which the use of 
commutator and brushes was restricted to the work of merely 
starting the armature, which when so started was then entirely 
short-circuited on itself, though disconnected from the rest of 
the circuit. It thus operated purely as a monophase induc¬ 
tion motor. A motor of this kind was shown at the Paris 
Exposition of 1889. In 1892, Elihu Thomson patented an 
alternate-current motor, for use with single-phase circuits, in 
which a rotatory effort, was produced by the use of auxiliary 
condensers shunting the coils wound on alternate poles. 

The Ferranti-Wright Motor .—If one end of a laminated 
bar of iron is placed in a magnetizing coil supplied with 
an alternate current, it will undergo an alternating mag¬ 
netization. But if at a point further along it is surrounded 
by a stout copper ring or ferrule, the eddy-currents in¬ 
duced in the latter, being out of phase with the primary 
current, will react locally on the alternating magnetization, 
and retard the phase of the magnetic polarity at all points 
beyond. Consequently, if two or three such closed rings 
or bands of copper surround the iron core at different 
distances along, the effect will be the same as if the poles 

1 Elihu Thomson, “ Novel Phenomena of Alternating Currents,” Elec. 
World (N. Y.), ix. 258, May 28, 1887; xiv. 231, October 5, 1889. 


Miscellaneous Alternate-Current Motors . 173 

travelled along the iron at a finite speed, a north pole being 
followed by a south pole, and again by a north pole, each 
travelling toward the tip, and there dying out. On this plan 
the Ferranti-Wright motor is based. It is used in Ferranti’s 



Fig. 148. Fig. 149 


alternate-current meters. A pivoted iron disk is placed 
between two curved pole-pieces of laminated iron, each of 
which is furnished with retarding-rings of copper, as shown in 
Fig. 149. 

Shallenberg's Motor .—This motor, which is used in an 
alternate-current meter, produces the rotation of an iron 
disk by a very neat method of splitting the phase of the 
alternate current. The disk is placed between two coils with 
a rectangular opening, within which, and also passing over 
and under the disk, is a closed coil, or rather stamping of 
copper, set obliquely at about 45° with the main coil, from 
which it receives induced currents. If it lay parallel to the 
main coil it would receive stronger induced currents, but 
would produce no rotatory effect. If it lay at right angles, it 
would receive no currents, and therefore also have no rotatory 
effect. As its currents are a little retarded behind complete 
opposition of phase, its oblique position gives a component 
to the resultant field producing rotation; but the resultant 
rotatory field is in reality an elliptical one (see p. 64 above). 

Atkinson's Motors .—In 1888 1 Mr. Llewellyn B. Atkinson 
(of Messrs. Goolden & Co.) devised some alternate-current 
motors which had the feature of two rotors (or amatures) side 
1 Specifications of Patents, 16,852 of 1888, and 7895 of 1889. 



















*74 


Polyphase Electric Currents . 

by side, interconnected in tlieir (closed) windings, and two 
separate stationary parts with windings into which the 
alternate current was brought. Each rotor served alternately 
as a transformer to send current into its neighbor’s windings, 
so producing a rotatory effort, though there is no rotatory field. 

The Stanley Kelly Motors .—Mr. William Stanley, of Pitts¬ 
field (Massachusetts), who was associated with Mr. Westing- 
house from 1886 in the development of alternate-current 
machinery, has devised a two-phase system, 1 in which the 
generator is of the “ inductor ” type, the only revolving part 
being a steel wheel with polar projections of laminated iron. 
The Stanley-Kelly-Chesney motor used with this system 
differs radically from the majority of those described in this 
work ; for in it there is, in truth, no rotating field at all. The 
stator into which the 2-phase currents are led consists of 
two entirely separate parts, each of which is separately sup¬ 
plied by one of the two currents. There are therefore pro¬ 
duced two simply alternating independent magnetic fields 
with a 90° difference of phase between them. Within these 
two stators, which are fixed side by side, there revolve two 
rotors mounted side by side on the same shaft. The windings 
of these rotors are so interconnected that the wire which lies 
directly under the poles on one armature is in series with the 
wire that lies between the poles in the other. So connected 
each rotor acts alternately as a motor to receive current and 
be driven by it, and as a transformer to send current to the 
other. The windings on the two rotors together are closed, 
having no external connections by slip-rings or commutator. 
It is claimed that these motors will give a torque at starting 
from li to 2 times as great as when running at full load. 
Condensers are used in parallel with the stator circuits to 
furnish at starting the idle current, and prevent the inductive 
drop in the pressure. A resistance is inserted in the circuit 
at starting. 

T. Duncan’s Motor .—This is a form intermediate between 
Shallenberger’s and Ferranti’s, the oblique coil of the former 


1 Electrical World , p. 325, 1893. 


Miscellaneous Alternate-Current Motors. 

being replaced by an oblique iron core surrounded near its 
extremities with throttling circuits of copper. It is applicable 
to three-phase circuits, and is intended for use in meters. 

Mordey's Motors. —Mr. W. M. Mordey has designed vari¬ 
ous forms of alternate-current motor. In one of these—a 
motor with laminated iron throughout—he proposes to pass 
part of the alternate current through a commutator on the 
shaft for the purpose of exciting the field-magnet, so that as 
the motor acquires speed the frequency of the alternations of 
current in the motor itself is reduced until synchronism is 
attained, when the current, so far as the magnet itself is con¬ 
cerned, becomes unidirectional. 

Gianz's Motor .—A similar proposal emanated from Messrs. 
Ganz and Co., of Buda-Pesth. 

W. Landon-Davies 1 s Motor .—This is a form of split-phase 
motor having two or more sets of coils placed at differ¬ 
ent angles ; the windings being calculated so as, while 
producing equal ampere-turns, to have phase-angles which 
are the supplements of the position angles of their respective 
coils. 


176 


Polyphase Electric Currents. 


CHAPTER X. 

POLYPHASE TRANSFORMERS. 

The principles underlying the transformation of polyphase 
currents to currents at a higher or lower pressure, hardly differ 
from those involving single-phase currents. The law which 
states that the ratio E x / E 2 between the electromotive-forces 
in the primary and secondary is equal to the ratio between 
the number of winding Si / S 2 , is of course applicable to every 
case of coils wound upon the same magnetic circuit, and the 
laws relating to the losses in the copper and iron are appli¬ 
cable to polyphase and single-phase currents alike. Indeed, 
the transformation of polyphase currents might be carried out 
entirely by means of ordinary single-phase transformers, it 
being only necessary to place a transformer in each of the 
polyphase circuits to raise or lower the tension to any desired 
extent. It is, however, convenient to have one transformer 
for all the circuits, and a saving in material is effected by so 
doing. In the case, for instance, of 3-phase working, just as 
three of the six wires originally employed can be dispensed 
with and a saving in copper Effected by joining the three 
circuits to a common junction, so there is a corresponding 
saving in iron by having a common junction at each end of 
the cores wound with the various circuits of a transformer. 
Fig. 150 shows diagrammatically a transformer in which the 
cores ABC are so joined to a common junction at each end. 
In order that the cores may be properly laminated, it is 
easier to build them of iron stampings of the forms shown in 
Figs. 151 and 152. If the coils are wound around A, B and C, 
the flux in these cores will follow a law similar to that of 
the circulating currents ; that is to say, it will be a 3-phase 
flux, there being a difference of 120° between the flux-phase 


Polyphase Transformers. 


T 77 


of each limb. It will be seen that the portions D', D" and 
D'" in Fig. 152 form a mesh-connection of the paths A, B 
and C ; there will therefore be a difference of 120° between 
their respective flux-phases ; and generally it may be said that 
Fig. 55 (p. 46) which shows the relations both of magnitude 
and phase of the currents in a mesh-circuit is equally applicable 
to the fluxes in the various parts of the core shown in Fig. 152, 
where A, B and C take the place of the line wires, and D', 




Fig. 151. 



Fig. 150. 

D" and D r,r the phase of the limbs of the mesh. We may 
take D' D" and D w as the cores of transformer instead of A, 
B and C, or we may wind both or either set with primary or 
secondary coils, and as such coils may themselves be joined 
up in star or mesh, a great number of combinations and per¬ 
mutations are possible. 

The transformers actually employed in 3-phase work¬ 
ing usually consist of three vertical columns of laminated iron, 

x2 





















178 Polyphase Electric Currents . 

having common yokes across the ends ; the primary and 
secondary coils being wound in the usual manner over the 
vertical parts of the core. Fig. 158 illustrates a 3-phase 
transformer made by Messrs. Siemens and Halske of Berlin. 
The transformers used in the famous Lauffen-Frankfort 
transmission of 1891, and Still used in the supply of 3-phase 

current to the town of Heilbronn, are 
illustrated on p. 386 of the Official 
Report referred to above (see p. 106). 
They were designed for the purpose 
of transforming from 15,000 volts 
to 100 volts, or vice versd , but ad¬ 
mitted of various groupings. The 
arrangements of the circuits was 
illustrated in Fig. 103, p. 107. The 
common junction of both the high- 
pressure and low-pressure windings 
was in every case put to earth. 

For 2-phase transformation two 
separate transformers might be used, 
one in each circuit. But just as in 
the circuits themselves there is some 
saving of copper by combining them 
so as to employ three lines instead 
of four (one of slightly greater sec¬ 
tion serving as a common return 
for the other two); so there is a 
saving in combining the two iron 
circuits in one, having in one part a common core. The 
appropriate arrangements and connections of the windings 
are shown in diagram in Fig. 154, 

The proper cross-section for the common core is |/2 times 
that of the separate cores, if the same maximum of flux- 
density in the iron is to be attained. 

In those cases where a mesh-grouping is adopted in a two- 
phase generator the circuits are not capable of being used 
with a common return ; two separate lines must be used for 
each circuit. But if transformers are used at both ends of the 



Fig. 153.— Three-phase 
Transformer con¬ 
structed by Siemens 
and Halske. 






























Polyphase Transformers . 179 

transmission, three lines only are needed. This disposition, 
which is shown in Fig. 155, was used by Schuckert & Co. at 
Frankfort in 1891 in one of their transmissions of power. 




Fig. 155. 


Phase-transformation. —So far we have dealt with the 
problem of transforming the voltage of a given system of 
currents. But there is another problem needing solution, 
namely, that of transforming 2-phase currents into 8-phase, 
or vice versa. 

The simplicity with which this problem can “be resolved 
will easily be understood by further developing the ideas un¬ 
folded above. 

When a transformer of the type shown in Fig. 152 is in 
action, the field is in the nature of a rotatory one. The core 
is in the shape of a wheel with three spokes. If we increase 
the number of spokes as shown in Fig. 156 we get a more 
uniformly rotating field. 

We may have as many spokes as we like wound with 














































180 Polyphase Electric Currents . 

primary coils, and we may divide the rim of the wheel into as 
many portions as we like, each wound with a secondary coil, 
and thus we may transform from a system of currents of any 
number of phases to a system of any other number, provided 
we start with something more than a 
single phase, so as to obtain a rotatory 
field, and not a merely alternating one. 

The same result can also be effected 
by dividing the rim into a certain 
number of parts wound with primary 
coils, and into a different number of 
parts wound with secondary coils. In¬ 
stead of spokes, in such a case the centre 
would be filled up with iron, leaving 
gaps just sufficient for the windings. It is not even neces¬ 
sary to have primary and secondary coils. If there be 
one closed winding on the rim, like the winding of a 
Gramme ring, and wires of one system of currents be con¬ 
nected successively at equal intervals all round to this winding 
it is possible to draw off a system of currents of any other 

number of phases by merely 
joining the required number of 
wires to the winding in the same 
manner. The first suggestion 
for transforming from 3-phase 
to 2-phase on this plan was 
made by the author at a lec¬ 
ture delivered at the Royal 
Institution, Feb. 23, 1894, on 
the transformations of electric 
currents. On that occasion a 
ring-transformer having twelve 
coils in closed series was joined 
to a 3-phase supply at three equidistant points, A, B and C. 
An alternate current could be taken off from the two ends 
of any diameter across the windings, as from A A,, whilst at 
the same time another alternate current, of voltage equal 
to the former, could be taken off at the ends of a diameter 



jA 

Fig. 157. 




Polyphase Tvans formers, 181 

D D y at right angles to A A ; . As in this case the 2-phase 
coils subtend 180°, while the 8-phase subtend 120°, the rela¬ 
tive voltages will be as 1 : 0-75, being proportional (if the 
distribution of the magnetic flux follows a sine-function around 
the periphery) to 1 - cos ; where /3 is the angular breadth. 

By such an apparatus any desired phase-transformation 
might be effected. The magnetic circuit is greatly improved 
by providing an iron centre-piece, properly laminated, whether 
stationary or revolving. 

A few days later, on March 1st, 1894, at a meeting of the 
National Electric Light Association, at Washington, Mr. C. F. 
Scott, chief electrician of the Westinghouse Company, pro¬ 
posed a different solution of the same problem, requiring the 


A 



use of two transformers. As arranged for transforming from 
2-phase to 3-phase it is described as follows: — “ The 
primaries of two transformers are connected to a generator 
giving 2-phase current. The secondary electromotive-forces, 
therefore, differ 90°. One secondary is made equal to 100 
turns, and a loop is brought out at its middle point, giving 
50 turns at each side. The second secondary has 87 turns, 
which is approximately 50 multiplied by the square root of 
3. One end of the secondary circuit is connected with 
the middle point of the secondary of the first transformer, as 
shown, and the three free terminals will then deliver electro¬ 
motive-forces differing in phase 120°. If the electromotive- 
force on each primary be 1000 volts, and on one secondary 











182 


Polyphase Electric Currents . 

100 volts, and on the other 87 volts, then the electromotive- 
force measured between any two secondary terminals will be 
100 volts.” 

Methods of Transforming ( Single-phase ) Alternate Currents 
into Two-phase or Three-phase .—The following method of ob¬ 
taining 3-phase currents out of 2-phase is due to M. D 6 sir 6 
Korda. It consists in principle of a transformer with three 
cores, and of a movable self-induction coil. The circuit 
carrying the monophase current, c = C sin pt , is divided 
into two branches I. and II. having the same ohmic resist¬ 
ance. A self-induction coil is inserted into branch II. in 
order that 

L /= 4/3 = tan 60°. . . ( 1 ) 

it 

The current in branch I. may be expressed by 

E . . 

ci= sin pt. 


The current in branch II. is expressed by 
E 

sin (pt —©) 


VlVXf L 2 
E 


= 2Tt shl 


That is to say, c 2 will be one-half of current c so long as 
equation (1) is satisfied. If the branch II. contains n turns 
on one of the cores of the transformer, the branch I. must 
contain % n turns wound on the second core, and the directions 
of the windings are opposed to each other, so as to produce 
an equal flux in each core, differing in phase by 120°. The 
third core of the transformer is wound with both branches, the 
direction being such as to produce a third flux, differing again 
by 120° from the other two. Three-phase currents are then 
obtained from secondary currents wound on the three cores. 

Methods of Transforming Continuous Current into Poly¬ 
phase Alternating Currents, or vice versd .—The methods 
of transforming continuous currents into simple alternat- 




Polyphase Transformers . 183 

ing currents, or vice versa :, are applicable also to polyphase 
currents. For brevity we may write A C for alternating 
currents, C C for continuous currents, and P C for polyphase 
currents. 

The oldest method of transforming C C to A C or vice 
versd, is by coupling together two machines, one of each kind, 
the one as motor to drive the other as generator. An example 
of this exists at the town of Cassel, which has a continuous 
current three-wire supply (with accumulators) fed from C C 
dynamos which are driven by A C synchronous motors re¬ 
ceiving single-phase alternate currents at a high voltage from 
a distance. 



Fig. 159. 


In the second method, an armature revolving in a mag¬ 
netic field receives C C to drive it as a motor, and gives out 
A C by means of slip-rings suitably connected to the same 
windings. Fig. 159 illustrates this mode of transformation, 
which can also be used for the converse change of A C into 
C C. In the drawing the revolving armature is shown as a 
simple coil with a two-part commutator for the C C connec¬ 
tions ; but in practice a more complex armature with a many- 
part commutator is employed. For example, an ordinary 
Gramme ring is used, with the addition of two slip-rings, 
which are conducted to two points 180° apart. Such a 
machine has been in use at the Technical College, Finsbury, 
since 1885, when the rings were added by Dr. Walmsley. It 
























184 


Polyphase Electric Currents . 

will serve as a transformer either way, or, if driven by power ? 
will furnish either kind of current, or both at once. In 1887, 
a patent was taken out by the Helios Co. for this very com¬ 
bination : and in 1889, Mr. Bradley and Mr. Tesla patented 
similar devices. For producing 3-phase currents from C C, 
three slip-rings must be connected on at three symmetrical 
points. For two-phase currents four slip-rings are connected 
at points 90° apart. In a recent apparatus of Hutin and 
Leblanc 1 a row of eighteen slip-rings are connected at as 
many symmetrical points, giving rise to eighteen alternate 
currents, each differing in phase by 20° from its next 
neighbor. 

A simple revolving combined commutator, like that of 
Fig. 159, would suffice to convert C C into A C, or to rectify 
A C into C C, without any field-magnet, were it not for the 
practical difficulties arising about sparking. The use of the 
field-magnet is to balance the electromotive-forces in the dif¬ 
ferent parts of the windings, as well as to maintain the 
proper rotation. 

At the Frankfort Exhibition of 1891 many revolving 
transformers based on this plan were shown. The firms of 
Lahmeyer and Schuckert, in particular, displayed many very 
interesting forms of polyphase apparatus, in which this feature 
was prominent (see p. 104). 

Messrs. Schuckert & Co. showed a six-pole ring-wound 
machine, capable of transforming from a continuous current 
or single-phase, 2-phase, or 3-phase currents to currents 
of any one or all of the other three kinds. It consists 
of an ordinary ring armature with a 144-part commutator, 
whose windings in front of the different pairs of poles are 
cross-connected in parallel (Mordey’s well-known method). 
As there are 144 sections in the winding, and six poles, the 
number of sections that lie between any pole and the next 
pole of the same sign, will be 48. From Nos. 1, 17 and 33, 
that is to say, at points equally spaced out at distances of 
one-third of the extent of the winding between any pole and 
the next pole of same sign, are attached three wires which are 
1 See an article in V Electricien of April 21st, 1894. 


Polyphase Transformers . 185 

brought down to three slip-rings, from which brushes supply 
3-phase currents. To four points also equally spaced along 
the same section of the winding (namely Nos. 1, 13, 25 
and 37), are attached four wires, which going to four other 
slip-rings, supply both single and 2-phase currents. 

Messrs. Schuckert have installed at Budapesth a station 
outside the town, from which power to the amount of 
1000 kilowatts is transmitted by a 2-phase system, at a 
pressure of 2000 volts, to several sub-stations in the town, 
and is there transformed into a continuous current. Each 
transformer is a double machine consisting of an alternate- 
current motor and a continuous-current dynamo mounted on 
the same shaft. The efficiency of transformation is 85 per 
cent. An installation has been erected by the same firm at 
Bilboa, in which a 3-phase generator is coupled direct with 
a turbine, and transmits 46 kilowatts to a station at a 
distance of two miles, where it is transformed into a continuous 
current. 

An eight-pole revolving transformer on a similar principle, 
but having a wave-wound drum armature, was shown at 
Frankfort by the Allgemeine Company. It could receive 
continuous current at about 100 volts, and transform this 
into 3-phase current at about 70 volts. This transformer 
is now in the laboratory of the Technical College, Fins¬ 
bury. 

M. Hospitalier has drawn up a general classification 1 of 
apparatus for effecting transformations of currents of one 
species to those of another, and designates such as polymorphic 
machines. 

At Dublin, an electric tramway using continuous currents 
at 500 volts is being worked by power transmitted by a 
3-phase system at 3500 volts. In this instance the transfor¬ 
mation is effected by motor-dynamos placed in sub-stations ; 
each machine consisting of a synchronous 3-phase motor 
rigidly coupled to a continuous-current generator. The 
machinery is supplied by the British Thomson-Houston Co. 

The subject of transformers would be incomplete without 
1 Societefranqaise de Physique , 1894, p. 203. 


186 Polyphase Electric Currents . 

a reference to the auto-transformer used sometimes when a 
smaller electromotive-force is required for a short time, as in 
the case of the starting of a motor. The auto-transformer 
(or “ one-coil ” transformer) merely consists of a coil of wire 
wound on an iron core, and connected across the mains. To 
some point in it, at a greater or less distance from one end, 
according to the voltage required, a branch wire is attached 
and current is drawn off between this branch and one end. 
It will be seen that a much greater current can be drawn off 
in this way than is actually supplied by the mains, as the 
piece between the branch and the end in use acts as the 
secondary of a transformer. 

Polyphase Choking-Coils .—Polyphase choking-coils can be 
constructed upon the plan of polyphase transformers by using 
one set of windings (in two or in three phases) upon the cores 
in lieu of the primary and secondary windings. The ordinary 
rules for winding choking-coils apply, due regard being had 
to the groupings of the phases. 


Measurement of Polyphase Power . 


i8 7 


CHAPTER XI. 

MEASUREMENT OF POLYPHASE POWER. 

As is well known, the power given by an alternate current 
to any part of a circuit may be measured in several ways: 
by the use of a watt-meter; by the method of the three volt¬ 
meters ; or by several analogous methods. 1 

In the case of 2-phase and 3-phase systems there is some 
complication. In cases where the two or the three circuits 
are kept separate, a suitable watt-meter in each suffices ; and 
the total power supplied is the sum of the amounts measured 
separately. For example, in a three-phase system, arranged 
in either star or mesh, a separate measurement may be made 
of each limb of the circuit. 

It is obvious that in the case of 3-phase motors such 
a method of measurement would be highly inconvenient; 
and it is easily shown that a simplification may be effected. 

In the case where there is per¬ 
fect symmetry in the three circuits, 
it is obviously sufficient to measure 
with a watt-meter the power con¬ 
sumed in any one of the circuits, 
and multiply by 3 to ascertain the 
total power. But in any general 
distribution no such equality of 
consumption can be assumed to 
exist. 

Three-phase Power Measurement .—When we have three 
currents in three conductors, one of which is the resultant of 

iFor these the reader is referred to such works as Fleming’s Alternate- 
current Transformer , or Blakesley’s Alternating Currents of Electricity. 



i88 


Polyphase Electric Currents . 

the other two, and we have a corresponding relation between 
the pressures across the three conductors, it is evident that 
these six quantities are not independent of each other, and 
therefore it should be possible to measure the power without 
having to measure all six. 

Take the simple case of a 8-phase circuit of incandescent 
lamps joined in mesh-fashion, as in Fig. 160, where a, b and 
c are the lamp-circuits. Denoting by a, b and c the currents 
in these circuits, and by V qr and V rp the pressures be¬ 
tween their ends, we have the total 'watts 

w = «y # , + jy (r + <f y ff . 

Taking the positive sense as indicated by the arrows in 
the figure, we have at any instant 

y _i_ y _i_v —0- • V —-V —V 

substituting in above 


W = — a V qr — a V rp +6 V gr +c V rp 
= V qr (b-a) -{- V rp 0 —a). 


If jt?, q and r are the currents in the mains leading into the 
mesh, then ( b — a ) = and (<? —a) = — p ; therefore 

W = V qr q-Vr P p- 

This expression appears to be the difference of two 
quantities of power on account of the sense chosen as positive 
in the figure if we reverse the sense of the pressure between 
r and p ; then as V rp = — V p r , 

W = V qr q+ V pr p- 

That is to say, if we pass the current q through the series 
coil of a watt-meter whose shunt coil is connected between 
q and r, and pass the current p through the series coil of 
another watt-meter whose shunt coil is connected between 
p and r, then the sum of the watts registered by the instru¬ 
ments is the total power absorbed in the circuits a, b and c. 

If the circuits form a star-grouping a similar formula can 


189 


Measurement of Polyphase Power. 

be deduced. Employing the letters of Fig. 54 (p. 46) we 
have the total watts 

W = V jm aXV jn bXV jo c. 

Taking now the currents, instead of the pressures as in 
the case of the mesh, 

a + 5 -{- c? = 0; a — — b — c. 

Substituting as before and noting that 

— = V.. and V JO — V,„ = V mo 

we get 

W = v mn b + V mo e. 

Two watt-meters of suitable construction suffice, therefore, 
to measure the power. Dr. H. Aron 1 has constructed a meter 
suitable for measuring the consumption, the design of the 
instrument being a modification of his well-known pendulum 
meter with differential gearing. The 8-phase meter has 
its second pendulum accelerated by the two movable coils 
of the two watt-meters, each moving coil lying within its 
corresponding fixed coil. 

Other forms of polyphase meter have been proposed by 
T. Duncan, 2 and by Shallenberger. 3 

1 Elektrotechnische Zeitschrift, xiii. 193, April, 1892. 

2 Specification of British Patent 6241, of 1893. 

3 Specification of British Patent 14S, of 1895. 


190 


Polyphase Electric Currents . 


CHAPTER XII. 

NOTES ON DESIGN OF ROTATORY-FIELD MOTORS. 

As with every class of machinery, so with polyphase motors, 
only practical experience can lead to excellence in design. 
All that can be given here is the fundamental argument upon 
which the general dimensions and winding of a motor de¬ 
signed for a particular purpose are based. 

The problem we have to consider is: Required, a motor 
of a given number of phases for a given voltage of supply, 
what shall be the dimensions of its parts and the number of 
its windings in order that it may yield a certain prescribed 
power ? 

Let us begin with the stator. The duties of the conductors 
of the stator (so far as the purposes of design are concerned) 
are (1) to provide a back electromotive force equal to V, the 
voltage of supply; (2) to carry a current in each circuit equal 

to • -, where W stands for total watts taken in at full 

V h cos $ 

load by the machine, and h is the number of circuits. The 
cosine of the angle of lag (cos <p) may be taken at 0*85. For 
instance, in the six horse-power 2-phase motor, shown in 
Plate I., intended for 100 volts, particulars of which are given 
on p. 211, taking the efficiency at 80 per cent, the watts 
absorbed at full load will be 5600. The current in each 
circuit will be 

5600 qq 

100 X 2 X 0-85 = 83 ampereS ‘ 

The smallness of the stator is limited by the fact that we 
have to get into it (preserving the proportions between iron 
space and copper space specified below) a certain total length 




Notes on Design of Rotatory-Field Motors . 191 

of active conductor which will perform these duties. The 
total length of active conductor in each circuit can be found 
from the equation. 

V-i> = £lU® 

10 8 ’ 

where V = pressure of supply in virtual volts. 

v = volts lost in resistance of stator conductors (see 
below). 

q = factor depending on the angular breadth of the 
coils (see p. 25), and may be taken as 0-9 
for a 2-phase motor like Fig. 97, and as 0-95 
for a 3-phase motor like Fig. 57. 

B = virtual flux-density (see belowj. 

A = total length of active conductor required, 
s = linear speed of magnetic field in cm. per second. 

The lost volts v ma}' be taken between 0*05 V for small 
motors and 0*02 V for motors of 100 horse-power and over. 

We have denoted by B the V mean sq. value of the flux 
density in the air space. As the maximum value of the flux 
density ought not to exceed 6000 lines per sq. cm. (which 
means over 11,000 in the iron between the holes), we may 
take 6000 -f- V 2, say 4200, as the value of B in the above 
equation. 

With regard to s it is difficult to lay down any rule, as it 
depends a great deal upon the purpose for which the motor is 
intended. The linear speed of the periphery of a rotor may 
be carried to a much higher point than is desirable in the case 
of an ordinary dynamo armature. While 1500 cms. per second 1 
is an ordinary speed for the periphery of a 100 horse-power 
armature, a rotor of this power may be run at 2400 cms. per 
second with equal safety. The linear speed of the periphery 
alters very little with the size of the machine, in fact 2000 cms. 
per second is a good useful speed for machines from 10 to 100 

1 Since 1 foot approximately equals 80 cm., it follows that a speed of 1 
cm. per second is approximately equal to 2 feet per minute. Hence 1500 
cm. per second is about equal to 3000 feet per minute. 




192 


Polyphase Electric Currents. 

horse-power, though it may be increased considerably beyond 
this for machines of very great radius. The speed s of the 
magnetic field is from 2 to 5 per cent, higher than this, accord¬ 
ing to the amount of slip. The radius of the rotor, for reasons 
which will appear later, varies very nearly in proportion to the 
square root of the horse-power. From a comparison of the 
dimensions of well designed polyphase motors it appears that 
the formula 

r = 200 

' s 

gives us in centimetres the length of the radius suitable to 
form the basis of the design. This formula is based on the 
comparison of motors intended fora frequency of about forty or 
fifty periods a second. For higher frequencies sufficient data are 
not available, but as theoretically the frequency does not affect 
the size of the motor, it would seem that the general method 
of design indicated here is applicable to frequencies as high as 
100 per second. Of course a wide departure from the radius 
calculated as above would be admissible. If on roughly 
calculating out the dimensions the length of the rotor in the 
direction parallel to the shaft came out too long, it is easy to 
assume a larger radius than the formula gives, and recalculate 
from this point onwards. A suitable number of revolutions 

320 

per second (here denoted by n{) will be about-! The 

r 

frequency of alternation of the supply we will denote by n. 
The number of pairs of poles produced b}^ one circuit of the 

stator (carrying one of the polyphase currents) will be E 

n 2 

where n t is the number of revolutions of the field per second. 

This ratio — must be a whole number, and we can therefore 

n 2 

take it as the whole number which will make n 2 as nearly as 
possible equal to 1-03 n x (allowing a slip of three per cent.). 
The linear speed s will then be 2 * n 2 r. Of course a maker 
may modify this calculation by other considerations, as, for 
instance, when he has already iron stampings in stock which 
will do for the motor. 




Notes 07i Design of Rotatory-Field Motors . 193 

Having fixed s we have all the data from which to calcu¬ 
late A, and upon this and the cross section of the wire the 
breadth of the stator depends. 

The diameter of the conductor may be chosen so that the 
current density amounts to between 250 and 300 amperes per 
square cm., according to the mode of insulation and facility for 
cooling. We will denote by a the area occupied by the cross 
section of a conductor, including insulation and space lost in 
packing. 

Next we have to consider into how many pieces the total 
active conductor in one circuit shall be divided. The total 
space available for the stator conductors will depend upon the 
radial depth d of the winding (see Fig. 105). 

It is desirable to make d as small as possible, for the 
greater it is the greater will be the amount of magnetic 
leakage. In general it may be taken as twice the breadth of 
a hole, though this will be subject to modification to suit other 

matters in the design. We have seen that — is the number 

n 2 

of pairs of poles, and from this and the number of phases the 
number of holes can be settled. For instance, if the winding 
is to be like that shown in Fig. 171, and the number of phases 
is two, taking the frequency n at 50 and n 2 at 5, the number 
of coils in each circuit will be 20, that is 40 coils in all. 
The question how many holes we shall allow for each coil (or 
for each wave if a wave winding is adopted) depends upon the 
diameter of the stator and the number of coils or waves. We 
cannot do better than follow the example of such designers as 
Mr. C. E. L. Brown, and make the iron between the holes 
about the same breadth as the holes themselves. This will 
mean that where there are only a few coils, as in the four-pole 
motor, Plate I., a number of holes (four in the figure) will be 
assigned to each coil; where, on the other hand, the number of 
coils is great, as in Fig. 171, two holes only will suffice for 
each. The object in view is to keep the winding as near to 
the surface of the stator as possible. Having ascertained the 

most suitable number of holes ( g ) the breadth of each is —, 


13 


194 


Polyphase Electric Currents . 


and taking d as twice the breadth, we have the area nearly 
0 2 2 

= . 71 r - . From this we must allow a certain area for the 

9 % 

paper tube or other insulation, and then we have left the 
available area A of each hole. 

We then have ^ as the number of conductors through 
a 

A 

each hole, and x — = total number of conductors in one 
h a 

circuit. Therefore the length of each conductor must be 

l in centimetres = A . 

9 A 


This gives us the breadth of the stator face. It will be 
seen that the last variable that we have taken, the one in 
fact which finally adjusts the machine to the desired voltage, 
is the length of each active conductor, or, what is the same 
thing, the measurement across the stator face parallel to the 
axis. This is a measurement which can be varied consider¬ 
ably in its relation to r without interfering either with the cost 
per horse-power or the efficiency of the machine. It will be 
found, however, that in large machines it is always made 
smaller in proportion to r than in small machines. As the 
stator is built of laminated iron clamped together, there are 
mechanical reasons why its breadth should not be great as 
compared with its radial depth. It is partly on account of 
this that we find the radius of the rotor varies as the square 
root of the horse-power rather than as the cube root. The 
radial depth is about one-half of the breadth of one pole. 
The fact that the radial depth d of the stator holes decreases 
in its relation to the radius as the radius is increased, causes 
the stator breadth to increase a suitable amount as the size of 
the machine is increased, for the power of the machine is 
roughly proportional to the weight of copper in the stator. 

The dimensions of the stator having been fixed, those of 
the iron work of the rotor immediately follow. The total 
breadth of laminated iron in the direction parallel to the axis 
is the same in each. The air space between the two is made 



Notes on Design of Rotatory-Field Motors . 195 

as small as possible, allowing just enough room for the rotor 
to run clear under practical working conditions. In the 
motor shown in Fig. 105 the air space is only 0*5 mm. across, 
that is to say, the outside diameter of the rotor is 1 mm. less 
than the inside diameter of the stator. In small motors of 4 
or 6 poles the rotor is built up of disks, such as that shown 
in Fig. 105. When the poles are numerous, the centre portion 
of such disks would be inoperative ; the laminated portion of 
the rotor is therefore in the form of a ring, which may be 
built up of pieces of sheet iron, interleaved at the junctions, 
and bolted together on the rim of a cast iron support, which 
may be in the form of a wheel such as shown in Fig. 170. 

We have seen that it is desirable, though not absolutely 
necessary, to have the number of the conductors on the rotor 
incommensurable with the number of holes in the stator, so 
that there may be no tendency either at starting or at any 
speed below synchronism for the two to cog magnetically into 
one another. When the rotor bars are merely short-circuited 
at their ends with a solid ribbon of copper, no difficulty is 
experienced in choosing a suitable number. For instance, in 
Fig. 105 the number of stator holes is 40, and the number of 
rotor bars 37. 

When it is intended to connect the rotor bars in a regular 
winding, either for the purpose of inserting a resistance at 
starting or for the purposes discussed on p. 122, some dis¬ 
cretion must be used in the selection of their number. If, for 
instance, we intend to form three circuits to bring down to slip 
rings on the shaft, for the purpose of introducing resistance at 
starting, we may divide the space occupied by one magnetic 
pole into three divisions 1, 2 and 3. All the conductors in 
division 1 in front of a North pole may be connected to con¬ 
ductors in division 1 in front of a South pole, and so on, 
forming a wave winding round the rotor; and the conductors 
in divisions 2 and 3 forming similar wave windings. If there 
are the same number of conductors y in each division, then the 
total number of conductors will be 3 y y where p is the number 
of single poles. This number will ordinarily have a common 
factor with the number of holes in the stator, but that in itself 


196 


Polyphase Electric Currents . 


will not prevent the motor from starting when the conductors 
are sufficiently numerous, and particularly if the numbers 
within the breadth of one pole are incommensurable. For 
instance, in the motor shown in Fig. 170 the number of holes 
in the stator is 80 and the number in the rotor 180 : the 
numbers in the breadth of a pole are 4 and 9 respectively. 

In fixing the cross section of the rotor bars it will be 
remembered that the greater it is, the greater will be the 
efficiency of the rotor, provided proper iron space is also 
allowed. There is nothing to be gained by making the total 
cross section greater than the total cross section of the stator 
windings, and in practice it is generally a little less. The 
current, per centimetre of periphery, in the one, is (neglecting 
magnetizing current) equal to the current per centimetre of 
periphery in the other. The conductors being of solid cop¬ 
per, and only lightly insulated, can be put into much less 
space than the stator conductors; and for this reason the 
holes in the rotor are usually smaller than one-half the size of 
those in the stator. 


Mechanical Performance of Polyphase Motors . 197 


CHAPTER XIII. 

MECHANICAL PERFORMANCE OF POLYPHASE MOTORS. 

The three chief requirements in the mechanical performance 
of a motor are (1) it shall exert a good torque at starting: 
(2) it shall be capable of running at nearly constant speed 
at all loads; (3) it shall yield in mechanical power a high 
percentage of the power put into it. 

The Starting of Polyphase Motors .—The conditions under 
which a great torque at starting can be obtained in a poly¬ 
phase motor have been considered in Chapter VI. The actual 
torque obtained of course depends upon the current which is 
passed through the stator coils. It may amount to four or 
five times the torque at full load. In the case of large motors 
it is undesirable to draw such a large current as would, if 
unrestrained, flow through the motor while it is getting up 
speed. The resistance inserted in the rotor circuit has the 
effect of keeping down the stator current by allowing the 
stator to act as a choking coil; its self-induction not being 
wiped out by the currents in the rotor, as would be the case if 
no resistance were inserted. At the same time a much 
greater torque is obtained, as shown in Chapter VI., than if 
the current were kept down by a resistance in the primary 
circuit. Fig. 161 shows a resistance composed of three vessels 
containing liquid to which the three wires from the rotor slip- 
rings are attached. The common junction consists of three 
plates, which can be raised and lowered in the liquid so that 
the resistance can be altered at will. In some cases the 
resistance is carried in the body of the rotor itself, and a 
device is mounted on the shaft for short-circuiting it after the 
motor has got up speed. For all small motors, and indeed 


198 Polyphase Electric Currents . 

for all sizes up to 10 horse-power, this arrangement is to be 
preferred, as it dispenses with all complications of slip-rings, 
brushes, and the like. Large motors are generally started 
light, and the load is gradually put on by belt-shafting or 
friction-pulley devices. For cranes, elevators, &c., special 
motors are made without collecting rings and brushes or any 
other means of inserting a resistance in the rotor circuits. 

These have a large armature 
slip (up to as much as 12 per 
cent.) and a low power factor, 
but they start with an initial 
torque equal to two or three 
times their normal load torque. 
The following table, supplied by 
Mr. Kolben, gives the current 
and voltage at the terminals of 
Fig. 161 . Dobrowolsky’s Start- a standard 9 horse-power crane 

ING-RESISTANCE. _ _ / _. ... 

motor, made by the Oerlikon 
Company, at starting with various loads. The pull between 
armature and field is not constant in all positions of the 
armature the minimum and maximum torque is therefore 
indicated. 

Starting Torque of 9 Horse-power Three-phase Crane Motor. 


Volts between 
neutral point 
and each 
terminal. 

Amperes in 
each branch 
at starting. 

Pull in kilogs. 

on lever of 

13 cm. at rest. 

48-5 

60 

15- 30 

58 

83 

30- 60 

69 

100 

50- 90 

75 

105 

60-100 

80 

115 

90-140 


The same motor, when running light at a speed of 1000 
revolutions per minute, with 110 volts pressure, took 20 
amperes. At normal load the current was 89 amperes and 
the speed 890, developing 8-5 horse-power. 


















Mechanical Performance of Polyphase Motors . 199 

Dr. Louis Bell, in a paper read before the American In¬ 
stitute of Electrical Engineers, January IT, 1894, 1 gives a 
number of useful experimental data as to ability of motors to 
start under load, the current required at starting, and various 
other matters. The curves in Fig. 162 are taken from his 
paper; they show the starting torque of a triphase 5 horse¬ 
power motor. B 2 shows the variation of torque with current 
for a given fixed resistance in the rotor circuit, the voltage 
being varied, and the resistance being such as to give a heavy 
torque. B 3 is the same as B 2 , except that the resistance was 
such as to give very moderate starting currents. The full 
normal load torque was 17*5 lb.-ft. It will be seen that the 




































2 













4 
















THE 

Load 

-< 

Xb 


























TorqpCs -lbs i A radius 
Fig. 162. 


motor when starting will develop full load torque on consid¬ 
erably less than full load current. With full load current, in 
fact, the torque at starting is 50 per cent, more than the running 
torque. Similar curves are given for a 10 horse-power motor, 
and also curves showing effect of varying the resistance. 

The Starting of Monophase Motors .—The methods by which 
a monophase motor may be started divide themselves into 

1 Electrical World, xxiii. 334-367, 400 (1894). 




















200 


Polyphase Electric Currents . 

two classes—(1) those in which a rotatory field is produced 
by an auxiliary winding on the stator carrying a current dif¬ 
fering in phase from the current in the main winding; (2) 
those in which the conductors of the rotor are connected (as 
by brushes on a commutator) so that the currents in them 
produce a polarity inclined to the polarity of the stator. 

The difference of phase in the currents in the two windings 
of the stator may be caused by the windings haying them¬ 
selves unequal coefficients of self-induction, or by putting re- 



Fia. 163.— Kolben’s Starting-gear for Monophase Motor. 


sistance or capacity in series with one, or inductance in series 
with the other; or any combination of these may be employed, 
as described on p. 156. 

Fig. 16B is a drawing of switch arrangements made by the 
Oerlikon Machine Company for the purpose of starting a 
motor. It is shown with the “ chopper” of the switch in the 
full-speed position. When in the starting position the blades 
of the chopper connect together the pieces c?, e and/ and also 
g with h. The points L x and L 2 receive the full pressure of 
the transformer, while L 3 is connected to the middle point of 
the transformer, so that between L x and L 3 there is a lower 




















































Mechanical Performance of Polyphase Motors. 201 

voltage than between and L 2 , but more current can be 
drawn without making a great demand on the mains. Con¬ 
sidering now the chopper in the starting position, the current 
after going from to c?, has two paths—one through e to the 
main coils, the other through/to the resistance coil and 
starting coils, returning by the pieces g and h to L 3 . After 
the motor has got up speed the chopper is thrown over, join¬ 
ing a to d and c to b. It will then be seen that the two wind¬ 
ings are in series, and take the full voltage of supply. 



Fig. 164. —Brown’s Starting-gear. 

In Fig. 164 is shown diagrammatically Mr. Brown’s method 
of starting a motor by means of an electrolytic condenser, 
(see p. 15T) marked K in the figure. The fine dotted line 
shows the connections of the chopper switch at starting, and 
the thicker line shows the same at full load. When the 
motor is not in use the chopper stands vertically. The coil a 
represents the ordinary working winding, and b the auxiliary 
winding, which in this case is cut out altogether after the 
motor is started. A 11 auto-transformer (see p. 185) is shown 
in the figure. 

In the specification of patent No. 24,098, filed December 
1892, Mr. Brown describes a number of methods of starting 
monophase motors, including the methods using auxiliary 
windings with self-induction and capacity, and also including 
some methods which fall under the second class described 
above. In these the rotor is wound as a Gramme or Siemens 
armature, with connections to a commutator, just as in the 
case of a continuous-current machine. Two opposite points 












202 


Polyphase Electric Currents . 

of the winding are also connected to two slip-rings. When it 
is required to start the motor a resistance is put between the 
brushes on these slip-rings, and the brushes on the commu¬ 
tator are placed so as to short-circuit a few of the windings 
of the rotor which lie obliquely across the direction of the 
alternating flux produced by the stator. The large ourrent 
in the short-circuited coils makes them turn so as to become 
parallel to the alternating flux, and the brushes retaining 
their position, a continuous torque is produced. As the motor 
gets up speed the brushes may be drawn further apart, until 
diametrically opposite. The brushes on the slip-rings are 
then also short-circuited. Mr. Brown also describes some 
methods in which the alternating current from the mains is 
supplied to the rotor through the commutator for the pur¬ 
poses of starting. 

Constancy of Speed .—As to the question of constant speed, 
we have seen that in a well designed motor the slip does not 
exceed more than 5 per cent, at full load, so the speed can 
only vary 3 or 4 per cent, between light load and full load. 
In a case cited by Dr. Louis Bell, an installation of IT rota¬ 
tory-field motors in Columbia, S. C., showed a maximum varia¬ 
tion in speed from an output of 75 horse-power to friction 
load of the motors of only 2 • 2 per cent., individual motors 
showing slighter variations down to li per cent. It is, how¬ 
ever, possible to vary the speed of a polyphase motor at will 
by inserting a rheostat in the main circuit. 

Efficiency .—The high efficiency of polyphase and mono¬ 
phase asynchronous motors will be seen from the following 
collection of data. 

Mr. Kolben has supplied the table opposite relating to 
some three-phase induction motors built by the Oerlikon 
Company. They have no collector-rings or brushes, no re¬ 
sistance being used in the rotor circuit. All motors have a 
drum-winding with 3, 5, 7 or 11 phases short-circuited in 
themselves. 

Mr. Kapp, in his book “ Electric Transmission of Energy,’" 
gives some data of two three-phase motors tested on a brake 
by Mr. Kolben, which are reproduced in the table on p. 204. 


Results of Brake Tests on Standard Oerlikon Three-phase Motors. 


Mechanical Performance of Polyphase Motors . 203 


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Kolben’s Tests of Three-phase Motors. 


204 


Polyphase Electric Currents . 



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Mechanical Performance of Polyphase Motors . 205 

The following are particulars of three-phase motors of 
various sizes built by the Allgemeine Elektricitats-Gesell- 
schaf t:— 


Types. 

D. R. 1. 

D. R. 5. 

D. R. 10. 

D. R. 50. 

D. R. 500 

Normal horse-power. 

1 


1 

2 

50 

Number of poles. 

2 

1 

4 

4 

8 

Weight in kilogrammes 

18 

65 

94 

245 

1200 

Current in each circuit at start- / 
i ng . \ 



20 

50 

400 

Current in each circuit at full i 
load . \ 

1-4 

4 

8 

36 

280 

Current in each circuit at no / 
load .j 



4-5 

15 

150 

Kilowatts absorbed at full load.. 

0-23 

052 

0*985 

4-38 

40-2 

Revolutions per minute at full | 
load . \ 

2300 

1400 

1375 

1395 

725 

Ditto at no load. 

2380 

1490 

1490 

1490 

745 

Ditto of field. 

3000 

1500 

1500 

1500 

750 

Slip-page at full load. 

23o/o 

v 8° /o 


7% 

3'3°/ 0 

Commercial efficiency. 


soil 

^0*75 

0-84 

091 

Torque in mk g . 



0-52 

2-6 

49-4 


The following interesting comparison between an 80 horse¬ 
power synchronous alternate-current motor installed in a 
corn mill, and a 100 horse-power asynchronous motor driving 
a spinning mill, was made by Mr. Kolben. The results are 
shown graphically in Figs. 165 and 166. 

The synchronous motor is of the Kapp type, with a flat 
disk armature, constructed by the Maschinen-Fabrik Oerlikon. 
It is wound for 2000 volts, with its shaft direct-coupled to its 
exciter. The E.M.F. curve is almost a sine curve. The 
asynchronous motor shown in Fig. 167 is an 18-pole high-pres¬ 
sure three-phase motor built by the same firm, for 1780 volts 
pressure at 50 periods per second, and arranged for rope 
driving at the low speed of 820 revolutions a minute. 

It will be seen from the curves that the power-factor of 
the synchronous motor is more favorable for all loads than 
that of the asynchronous motor, although the difference at 
full load is small, being 0*94 as compared with 0-86. The 
difference, for instance, with a loss on the line of 5 per cent., 
would scarcely bring about £ per cent, additional drop in 
the conductor. On the other hand the efficiency of the 























206 


Polyphase Electric Currents . 




Fig. 166 .— Three-phase Motor. 














































Mechanical Performance of Polyphase Motors. 207 


asynchronous motor is higher at all loads ; its curve is similar 
to those of a good transformer : it amounts at full load to 91 per 



cent., as compared with 86 per cent, of the synchronous 
motor. The total exciting energy, including losses in the 


Fig. 167.—18 Pole High-pressure Three-phase Motor. 



208 


Polyphase Electric Currents. 

exciter, is comprised in this, and, especially at small loads, 
reduces the efficiency. 

The efficiency of a monophase asynchronous 6-pole 15 
horse-power Brown motor, was tested by Ricardo Arno. 1 
The motor was built for a frequency of 40 cycles per second, 
but during the test the frequency was a little higher than 
this, the speed varying between 8T6 at no load, and 850 at 



full load. The power factor (cos 9) and the watts, real and 
apparent, supplied to the motor are also shown. 

M. Botcherot has given 2 tests of two Brown two-phase 
motors built by the Weyher and Richemond Company at 
Pan tin. One of these, of 2-8 horse-power, weighing 120 kilos., 
at 1125 revolutions per minute its efficiency was 76 per cent. 
A larger motor, of 17-20 horse-power, weighing 520 kilos., 

1 IS Elettricista, iii. No. 7, p. 149. 

2 Bulletin de la Societe Internationale des filectriciens , xi. 482, Dec. 1894. 






























Mechanical Performance of Polyphase Motors . 209 


had an efficiency of 90 per cent, at 770 revolutions per 
minute. 

A 50 horse-power Tesla 2-phase motor, built 1 and tested 
at the works of the Westinghouse Company, ran at 750 revo¬ 
lutions per minute, on 220 volts mains with frequency of 25 
periods. The speed falls only 2 per cent, from no load to full 
load. The efficiency is 84 at quarter load, and 89*5 at full 
load. The maximum starting torque is 2*5 times the torque 
at full load ; or, with a resistance in the secondary, 1-5 times. 
As the light-load efficiency is so high, this would be a most 
economical motor for all-day work on a variable demand for 
power. When running unloaded there is a nearly watt-less 
current of 62 amperes. 

Dr. Louis Bell, in his paper mentioned above, gives the 
following data as to weights per horse-power of rotatory field 
motors. 

Weight in 

Horse-power. lbs. per 

horse-power. 

5.103 

10. 66 

15. 68 

20 73 6-pole 

100 66 8-pole 


The following figures give the relation between weight and 
horse-power of standard motors of European make :— 


Horse-power. 

2 .. 

6 .. 
13 .. 

50 .. 
70 .. 
100 .. 


Weight in 
lbs. per 
horse-power. 

.. 120 
.. 100 
.. 88 
70 

.. 66 
.. 58 


These weights compare extremely well with those of con¬ 
tinuous-current motors; an ordinary 100 horse-power con¬ 
tinuous-current motor seldom weighing less than 80 lbs. per 
horse-power. 

Mr. Kapp has pointed out that as between a 2-phase motor 
and a 3-phase motor, the plant-efficiency of the latter is the 
better, its output being 111 as against 100 for a 2-phase 
motor of the same Aveight. 

1 Electricity , (U.S.A.), May 15, 1895. 


14 

















210 


Polyphase Electric Currents . 


CHAPTER XIY. 

SOME EXAMPLES OF MODERN POLYPHASE MOTORS. 

By the kindness of two of the firms which have been fore¬ 
most in the development of the polyphase motors, the author 
is enabled to describe several recent examples of this class of 
machine. 

Motors of the OerWcon Machine Company ( Zurich ).—From 
the autumn of 1891 the Oerlikon Machine Company has con¬ 
tinued to develop the rotatory field motor, and has made 
many hundreds of different sizes. In all small sizes, whether 
3-phase, 2-phase or monophase, the rotor is of the simple 
jquirrel-cage construction, while for the larger sizes wound 
rotors are used so as to enable resistances to be inserted at 
starting. So far back as July 1892, the engineers of this 
firm had succeeded by detailed improvements of construction 
in producing a 3 horse-power, 4-pole, 3-phase motor, with an 
efficiency of 71 per cent. The firm has adopted a standard 
frequency of 50 periods per second in its machines. The 
larger motors are generally arranged to start light on a 
loose pulley to avoid any great rush of current, since a high 
efficiency at full load, with small percentage of slip, involves 
a small starting torque ; but for cranes, elevators and the like, 
special motors are made (also without slip-rings or brushes) 
with a slip (at full load) of as much as 12 per cent. Their 
power-factor is consequently low, but they start with an initial 
torque equal to two or three times their torque at normal 
load. Some data of a crane motor were given on p. 198. 

A reference to this firm’s monophase motors, and the start¬ 
ing-gear used for them were also given above. 

The Oerlikon Company’s own works are driven by electric 


Some Examples of Modern Polyphase Motors. 211 


power transmitted some 14£ miles from a waterfall at Hoch- 
felden, near Bulach. The 8-phase machines by which this is 
accomplished were the first of their kind. There are three 
3-phase generators, each of 200 horse-power. They are 
depicted in Fig. 44, p. 38. They were designed by Mr. C. 
E. L. Brown, in the autumn of 1890, at the same time as the 
machine used in the famous Frankfort experiment of 1891. 
There is a similar transmission of 300 horse-power in Zurich 
from a waterfall at Killwangen, 12 £ miles distant. The 
power is distributed by overhead lines to numerous small 
motors. At St. Etienne, in France, there is a similar trans¬ 
mission of 1000 horse-power, and at Wangen, in Wiirtem- 
berg, of about 350 horse-power. 

Motors of MM. Brown , Boveri & Co .—Some mention was 
made on p. 118 of the earlier work of Mr. C. E. L. Brown. 
His firm has, since 1892, turned out a large amount of poly¬ 
phase plant, including generators and motors. By the courtesy 
of the firm several motors of modern design are here described 
in considerable detail. 

In Plate I. is shown, one-sixth full size, the elevation of a 
2-phase motor capable of yielding 6 horse-power. A sec¬ 
tional elevation is also shown in the plate, and the rotor and 
stator stampings are shown in Fig. 105. The winding of the 
stator is carried out in the manner described on p. 35, with 
the ends of the coils alternately bent sideways and arched 
over. In this particular motor, which is intended for a 
pressure of 100 volts and a frequency of 40 periods per 
second, there are 9 wires of 3-8 mm. diameter passed through 
each of the 40 slots in the stator. There are 37 round copper 
rods on the rotor, each 9 mm. in diameter, all short-circuited 
together at each end by a broad copper hoop, which, besides 
serving as a good conductor, presents a large cooling surface 
to the air. The air gap between rotor and stator is only 
0-5 mm. in breadth. The maximum value of B in the iron 
between the slots is 11,500, and in the iron behind the slots 
7500. The same carcase can be wound as a single-phase 
motor, and will then yield 4 horse-power. It will be seen 


2 X 2 


Polyphase Electric Currents . 


from the drawings that the bearings are of the self-oiling type. 
The following are some of the principal dimensions: 


Diameter of rotor . 

Inside diameter of stator. 

Radial depth of stator . 

Breadth of stator face . 

Radial depth of slots . 

Width of slots . 

Average width of iron between slots 
Diameter of holes in rotor 
Diameter of rods in rotor 


Centimetres. 
24-9 
25 

7 

11-5 
2*5 
1 
1 
1 

0-9 


Area of rods of rotor, in sq. cm. .. 
Area of conductor in stator, in sq. cm. 
Number of conductors per hole 


0-64 

0-13 


9 


Plate II. and Fig. 169 relate to a form of motor which has 
been constructed with different windings for different pur¬ 
poses. In the plate the windings are those of a 8-pliase motor 



taking current directly from high-pressure mains at 5000 volts, 
with a frequency of 40 periods per second and a speed of 600 
revolutions per minute. Its output is then 100 horse-power. 
Its height is 120 cm. or about 4 feet, and its length from 












Some Examples of Modern Polyphase Motors . 213 

outside of bearings is a little less. The diameter of the 
rotor is 75 eras., and its length, parallel to the shaft, is under 
45 cms. The rotor has 96 holes through which insulated 
copper conductors are threaded, to be joined up in a wave- 
winding constituting a three-branched star, of which the 
three outer ends are led down through the central hole bored 



Fig. 170.— Brown’s Slow-speed Two-phase Motor of 100 Horse-power. 

in the shaft to three slip-rings, so as to allow of an external 
starting resistance being applied. There are 48 holes in the 
stator core-rings, and through these the coils are wound, be¬ 
ing protected by strong tubes of prepared paper. The mode 
of arrangement of these coils to produce a 4-pole field is 
shown in Fig. 40. This motor starts under full load, taking 
less than full load current. 














214 


Polyphase Electric Ciirrent. 

The same framework, wound as a 2-phase machine at 2000 
volts, is shown in Fig. 169. It has an output of 120 horse¬ 
power. The stalling resistance in this case is placed inside 
the rotor, with a simple mechanism projecting out through 
the end of the shaft to short-circuit it when the motor has 


Fig. 171. —Stator of Brown’s Slow-speed Two-phase Motor. 

started. This device is seen on the right-hand end of the 
shaft in Fig. 169. 

In Figs. 170 and 171, is shown another 100 horse-power 
2-phase motor of different design, built by the same firm for 
running at a slower speed. This motor, supplied at a press¬ 
ure of 2000 volts (and frequency of 38 periods per second), 









Some Examples of Modern Polyphase Motors . 215 

runs at a speed of 200 revolutions per minute. Tested on 
a brake, it gave up to 200 horse-power before stopping. 
The stator coils, and the way in which the end connections 
are arranged, can be seen from Fig. 171. The plan of wind¬ 
ing is the same as that shown in Fig. 124, there being 28 turns 
in each coil. There are 40 coils (20 in each phase-circuit) 
threaded through 80 holes. In the rotor there are 180 con¬ 
ductors connected in three circuits, the ends of which are 
brought to slip-rings for the purpose of introducing resistance 
at starting. Motors of the same type are made for ordinary 
monophase supply, and at a pressure of 2700 volts will yield 
120 horse-power at 800 revolutions per minute. 

Brown’s motors are now extensively used for distribution 
of power in factories, the 8-phase current being particularly 
applicable to isolated plant of this description. The large in¬ 
stallation at Schonenwert, near Aarau, has been referred to 
on p. 87. 

Another example is furnished by the 2-phase distribution 
in the extensive engine-works of Weyher and Richemond 
at Pantin, near Paris. In these works there were formerly 
three separate steam-engines of 120, 80 and 50 horse-power 
respectively. These have now been replaced by a single 
horizontal engine of 200 horse-power (capable of working up 
to 400 horse-power), at 60 revolutions per minute. This 
engine drives three 2-phase generators, each of 88 kilowatt 
capacity, having revolving drum-wound armatures aud sta¬ 
tionary 8-pole field-magnets. The frequency is 40 periods 
per second. Usually only two of these generators are run, the 
third being a reserve machine. Down to the present time the 
number of motors installed in the different shops is 17, having 
a total output of 119 kilowatts, or about 150 horse-power. 
The outputs of these are as follows :—1 of 83 kilowatts, used 
for coal hoisting, 2 of 22 kilowatts, 1 of 14*5, 1 of 9*5, 1 of 
5-8, the rest of 2 kilowatts or under. Two still larger motors 
are now in course of construction. According to M. Boucherot, 
who has given 1 a full account of the plant, with views of the 
shops and machinery, the efficiency of the larger motors is 94 
'Bulletin de la Societe Internationale des Electriciens , xi. 482, Dec. 1894. 


216 


Polyphase Electric Currents . 

per cent., that of the smallest (IT kilowatt) 74 per cent.; the 
average efficiency of the motors taken all together being over 
89 per cent. M. Boucherot considers these machines to con¬ 
trast most favorably with continuous-current machines of 
equal power. The 2-phase motors, for equal efficiency, cost 
no more (including starting gear) than continuous-current 
motors, and run at a slower speed. The generators, for an 
equal efficiency, cost some 15 per cent, less than continuous- 
current dynamos of equal output. 

In Berlin the Allgemeine Elektricitats-Gessellschaft has 
developed the 3-phase motor for many purposes, notably for 
driving machine tools, centrifugal machinery and elevators. 
They have made a speciality of centrifugals in sizes varying 
from 1 to 7 horse-power. The largest are used in bread 
factories, whilst the smaller are employed in sugar refineries. 
For example, the sugar refinery of the firm of P. Schwenger’s 
Sohne, at Uerdingen on the Rhine, is fitted up throughout 
with electric motors to the number of 91, employing a total 
of about 490 horse-power. At the Breitenburger Cement 
Works at Lagerdorf are two 3-phase generators, each of 110 
horse-power, for transmitting power to elevators, pumps, 
stampers, and the like. The machine works of Colomna, in 
Russia, has a 3-phase plant of 600 horse-power for driving 
the machine-tools and cranes in its shops. Of the three- 
phase machines made by the Allgemeine Co. for the new 
central station at Strassburg some mention is made in the 
next chapter. 

The machinery in the workshops of the Westinghouse Co. 
at Pittsburg, U.S.A., 1 is driven by Tesla 2-phase motors; the 
installation, consisting of 39 motors varying between 10 and 
80 horse-power, having an aggregate of nearly 800 horse¬ 
power, Sixteen larger motors will shortly be added, increas¬ 
ing the capacity to double. The generators are of a new type, 
superior to that shown in Fig. 39, both circuits being connected 
to one winding after the manner shown in Fig. 96. The 
lighting of the shops is from the 2-phase circuits. 

1 Electricity (U. S. A.) vol. viii. 169, 185 (1895). See also the same 
journal, May 15, 1895, for efficency test of one the Tesla motors. 


Polyphase Currents from Central Stations . 


2i 7 


CHAPTER XY. 

DISTRIBUTION OF POLYPHASE CURRENTS FROM CENTRAL 
STATIONS. 

For the mere purpose of electric lighting, there is no great 
advantage in the use of polyphase currents as distinguished 
from ordinary single-phase alternate currents. But where 
other purposes are contemplated in an electric supply, par¬ 
ticularly the distribution of electric power, then the advan¬ 
tages of polyphase systems begin to appear. 

For many months the only example of a general distribu¬ 
tion of polyphase currents from a central station was that 
of the town of Heilbronn, which derives its 3-phase supply 
from the generating station at Lauffen, on the river Neckar, 
about 9 miles distant. The engineer who laid out the system 
is Mr. Oskar von Miller, of Munich, by whose courtesy the 
following information is supplied. 

The generators at Lauffen, the same that were used in the 
famous Frankfort transmission (Fig. 30), give each about 
4000 amperes at 50 volts. By a step-up transformer this 
supply is transformed into a current of 40 amperes at 5000 
volts, at which high pressure the currents are transmitted 
through three copper wires 6 millimetres in diameter, carried 
overhead on oil-insulators supported on timber poles. At 
Heilbronn these three currents are received by a step-down 
transformer, and transformed to about 133 amperes at the 
intermediate pressure of 1500 volts, at which pressure the 
cnrrents are distributed to the various quarters of the town. 
As a matter of fact there are three turbines (one for reserve), 
two generators, two step-up transformers, and two step-down 
transformers. The final transformation at Heilbronn, from 
1500 volts to 100 volts, is accomplished by small transformers 


218 Polyphase Electric Currents . 

of 5 kilowatts and 10 kilowatts capacity, which are placed in 
overground transformer-pillars at about twenty-five convenient 
points, and feed the low-voltage network that distributes the 
current to the lamps and motors of the consumers. Triple- 
concentric armored cables distribute current over about 
5 miles of streets. Arc lamps and glow lamps are used upon 
all three circuits, as well as motors. Down to the end of 1894 
there were the equivalent of 11,000 8 candle-power lamps 
upon the circuits, and 25 motors having a total output of 
about 53 horse-power. The small motors up to about 3 horse¬ 
power are arranged to be switched direct on to the circuits 
without any special starting gear. They are of the usual 
3-phase type with squirrel-cage rotors. The larger motors 
up to 8 horse-power are provided with starting-gear, including 
liquid resistances, so that the full current is not taken until 
some 15 or 20 seconds have elapsed, after which time they 
have got up their speed and are then switched over direct on 
to the mains. About half-way between Lauffen and Heil- 
bronn, at the hamlet of Sontheim, a few glow lamps in the 
streets are supplied by a transformer working direct from 
5000 volts down to 100 volts. No trouble is found to arise in 
the maintenance of proper regulation of the voltage in the 
three circuits. The motors tend to equalize the pressures and 
currents between the three circuits, though the numbers of 
lamps may be unequal. 

Amongst other polyphase stations at work are those of 
Dresden Railway Station, Chemnitz, Buda-Pesth, Strassburg, 
and Bockenheim. 

At Chemnitz, a municipal central station was equipped 
by Messrs. Siemens and Halske, in 1894, with a 3-phase 
system. The generators, of the “ R ” type, have an output of 
52 amperes at 2000 volts. They have an outer fixed arma¬ 
ture built up of core-rings, and an interior revolving star¬ 
shaped field-magnet with 40 poles of alternate kinds. At 
150 revolutions per minute the frequency of the alternations 
is 50 periods per second. The inner periphery of the arma¬ 
ture ring is slotted with 120 slots, or 3 slots per pole, to receive 
the windings. The slots are narrowed at their mouth to 


Polyphase Currents from Central Stations. 219 

receive wooden keys to hold in the windings. The windings 
are arranged as in Fig. 41, with their bent exterior portions in 
two planes, and all the coils of each phase are joined in series. 
One end of each of the three series is carried to a common 
junction, and the other three ends are brought out to three 
separate terminals on the machine. The winding is therefore 
a star winding (Fig. 58). One auxiliary coil on each generator 
furnishes a current to the synchronizing apparatus at 25 volts. 
There are three generators, each direct-driven by a triple¬ 
expansion condensing engine. If the excitation of the field- 
magnets is kept constant, the drop of voltage at full load on 
a non-inductive resistance is about T per cent. ; but when 
motors are being run on the circuit a much greater drop is 
liable to occur, requiring to compensate it an increase of 20 
to 80 per cent, in the exciting current. From the generators 
the currents are led through fuses and switches and measuring 
instruments to three omnibus bars on the switchboard, from 
which the high-pressure feeders go to the distributing mains. 
Triple-concentric cables, lead-covered and armored, conduct 
the currents at 2000 volts to transformers dotted about the 
town at twenty-four different points, where they are trans¬ 
formed to 120 volts for the low-pressure networks. There 
are about 6 miles of high-pressure cable, 12 miles of triple- 
concentric low-pressure cable, and about 4 miles of bare con¬ 
ductors. The furthest point is about 2 miles from the 
generating station, which is itself about 1 mile from the 
centre of the town. By the end of 1894 there were in use 
the equivalent of about 11,000 8 candle-power lamps, 160 arc 
lamps, and 80 motors of an average size of 2 horse-power. 
The motors have as stator a ring wound with coils in slots, 
similarly with the generators. The rotor is built up of iron 
core rings slotted on the external periphery, wound with 
coils, which are also joined up in a star grouping, and end at 
three slip-rings. These permit resistances to be inserted at 
starting and gradually cut out as the motor acquires speed. 
At full speed the rotor is short-circuited. A full description, 
with drawings, is given in the Elektrotechnische Zeitschrift y 
February, 1895. 


220 


Polyphase Electric Currents . 

For the city of Strassburg, of which Mr. Oskar von Miller 
is engineer, a 3-phase system has been adopted. The genera¬ 
tors, of the 44 inductor ” type, were built by the Allgemeine 
Elektricitats-Gesellschaft of Berlin, and are of 400 horse¬ 
power each. These machines are described by Mr. von 
Dolivo-Dobrowolsky in the Elektrotechnische Zeitschrift of 
February 7, 1895. 

At Bockenheim, an important suburb of Frankfort, is a 
3-phase station equipped by Messrs. W. Lahmeyer & Co. 
There are two direct-driven 3-phase alternators of about 150 
kilowatts each, of the same type as those used at Lauffen 
(p. 28), having fixed armatures and revolving field-magnets, 
but with only eight poles. They work at 80 volts, and 
their currents are at once led into 3-phase transformers re¬ 
sembling Fig. 153, to be transformed to 660 volts, at which 
high pressure they are conveyed by cables to the various dis¬ 
tributing points. For motor-driving the 3-phase motors are 
connected direct to the high-pressure mains. For lighting, 
transformers are interposed which reduce the pressure, and 
feed into a distributing network. Triple-concentric cables 
bring the currents into the houses. Asynchronous motors up 
to 20 horse-power are in use. They start under load, or even 
with an over-load. Those over 8 horse-power are, however, 
provided with loose pulleys so as to start on a light load. 
Water-resistances are used in the starting gear. Aron’s poly¬ 
phase meters are used. There is an independent continuous 
current supply in use for lighting only. Altogether the total 
consumption of power for motor purposes exceeds 200 horse¬ 
power. 

The regulation of voltage in the three circuits is not found 
to present any difficulty. If a star-grouping (like Fig. 67) is 
adopted in a 3-phase distribution, the fourth wire, which is 
brought back to the common junction of the three circuits of 
the generator, serves to equalize the pressures in case the 
numbers of lamps in the three branches are unequal. But in 
discussing the Chemnitz distribution it has been shown by 
Mr. Gorges that this is not necessary. A 3-phase equalizer 
can be added at some convenient point in the network, in 


Polyphase Currents from Central Stations. 221 

the form of a 3-phase transformer, each limb of which is 
wound, however, with but a single coil. It is, in fact, a three- 
phase clioking-coil or auto-transformer. These three coils 
are united in star-fashion, and the fourth wire of the circuits 
is brought to their common junction. Mr. Gorges states in 
one experiment 100 lamps were introduced in one of the 
three circuits, 20 in the second, and 1 lamp in the third, 
causing a very great inequality in the three voltages, until 
the fourth wire was joined to the mid-point of the equalizer, 
when at once the voltages became all alike. Three-phase 
motors inserted in the circuit have similarly an equalizing 
effect on the three voltages. Some years ago Mr. von Dolivo- 
Dobrowolsky noted the fact that 3-phase transformers also 
have a similar equalizing effect. 

At Buda-Pestli Messrs. Schuckert have a 2-phase station 
outside the city, as mentioned on p. 185. 

A 2-phase station has now been at work at Pittsfield 
(Massachusetts) for about two years, on the system of Messrs. 
Stanley, Kelley and Chesney. Another is in progress of 
development at Montreal. 

A list of 3-phase power stations which have been equipped 
by the Oerlikon Co. is given in the Table on p. 222. 

In the above enumeration no mention has been made of a 
very large number of isolated plants, in factories and the like, 
where polyphase methods seem likely to supersede all other 
modes of transmitting and distributing power. I 11 addition 
to those mentioned on p. 211 as having been carried out by 
the Oerlikon Co., and those of Brown, Boveri & Co. on p. 215, 
it may be noted that in Hellsjon, Sweden, there is a 400 
liorse-power transmission 1 of 3-phase currents over 8 miles, 
by machinery designed by the late Mr. Wenstrom. 

The “Monocyclic ” System. —Mr. C. P. Steinmetz has pro¬ 
posed 2 a system of distributing electricity for lighting and 
power which, although its essence is that more than one cycle 
or phase is used, is called the “ monocyclic ” system. By this 

1 See Gr. Kapp’s ‘Electric Transmission of Energy,’ p. 418, 4th edition, 
1894. 

2 See Electrical World , xxv. p. 182, Feb. 1895; also E. Boistel, “Distri¬ 
bution Monocyclique,” L' Eclair age Electrique , iii. p. 152, April, 1895. 


222 


Polyphase Electric Currents , 


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Polyphase Currents from Central Stations. 223 

system it is sought to obtain the advantages of a polyphase 
system for motor purposes, combined with the ease of regula¬ 
tion of a single-phase system. Under normal conditions the 
whole of the power is supplied by two mains, between which 
is maintained a constant alternating pressure. To those parts 
of the district where motive power is required, a third wire is 
carried, from which a current can be drawn, differing in phase 
from the main current, and by which motors can be started. 
The windings of the motor are arranged so that when full 
speed is attained the back E.M.F. is as great as the pressure 
from the third wire, so that no more current is drawn from it, 
the power being supplied by the principal mains. One of the 
ways of maintaining the difference of phase in the third wire 
is to wind on the alternator coils displaced in relation to the 
main coils, so as to generate an E.M.F. differing by 90° from 
principal E. M. F. One of the terminals of these displaced 
coils is joined to a middle point of the principal winding of 
the alternator, and the other to the third wire in question. 
The number of turns of the displaced coils is so arranged that 
the E.M.F. resulting from them and the half of the principal 
coils in series with them shall have the required difference in 
phase. Where a number of motors are installed, the back 
E.M.F. of any motor that happens to be running will be suf¬ 
ficient to start another motor, so that in cases where some of 
the motors are always running it will not be necessary to carry 
the third wire to the alternator. 

The monocyclic system is therefore really a three-phase 
distribution in which two of the phases are nearly in opposi¬ 
tion, while the third phase, nearly at right angles to the other 
two, is used as an auxiliary for starting motors. It cannot be 
maintained that this system, because it is not symmetrical, is 
not a polyphase system. 

The author has devised several other ways of attaining a 
similar end. One method is to use two alternate currents 
;itany phase-difference whatever between 90° and 120°, on an 
ordinary three-wire system of distribution, keeping constant 
the difference of potential between each and the middle w^ire. 
For motor-starting a third circuit is obtained from the two 


224 


Polyphase Electric Currents . 


outer wires, which will yield a current out of phase with the 
other two. The exact phase and exact potential of this third 
current is immaterial: the motors used may be either 3-phase, 
or 2-phase with a common return. 

Another unsymmetrical system has been proposed by 
Mr. Imhoff. 

Where ordinary single-phase currents are supplied on a 
three-wire system, as in the City of London, it is exceedingly 
easy to introduce a phase-difference into the middle wire, 
enabling motors to be started and run. In fact, if a single 
3-phase motor is started on any such circuit, it will help other 
motors on the same circuit to start, as it will itself tend to 
preserve the requisite differences of phase. 

An American example of 3-phase lighting, at Concord 
(N. H.) is described in the ‘ Western Electrician ’ of Feb. 16, 
1895, and another at Winooski (Vt.) in the ‘Electrical 
Engineer,’ June, 1895. 

At Baltimore there is now a 2-pliase station furnished 
with four Westinghouse alternators, each of about 1000 kilo¬ 
watts output. They are direct-driven, and will be largely 
used for arc lighting as well as for glow-lamps. Tesla two- 
phase motors will be used. 

The largest plant in the world for the supply of electric 
currents is a polyphase plant—namely, that established at 
Niagara (see p. 39)—using a 2-phase system of currents. It 
will begin operations at an early date. 

Recent as have been these inventions and rapid as their 
development ha ^proved, it is already evident that their indus¬ 
trial aspect is settling down upon well-defined lines. Yet 
finality is far from having been attained. The problems of 
the conversion of electric currents from the alternating to the 
continuous varieties are still in progress of solution. What 
results the newest methods of transformation may bring about 
none can foresee. The next few years may witness develop¬ 
ments at present quite beyond the contemplation of the electric 
engineer. 


APPENDIX I. 


BIBLIOGRAPHY OF POLYPHASE CURRENTS AND 
ROTATORY-FIELD MOTORS. 


a. BOOKS AND ARTICLES. 

Offizieller Bericht tiber die Internationale Elektrotechnische 
Ausstellung in Frankfurt am Main. J. D. Sauerlander, Frank¬ 
furt, 1893-4. 2 vols. 

Sahulka, J. Ueber Wechselstrom-Motoren mit magnetischem 
Drehfelde. Deuticke, Wien, 1892. 

Picou, R. V. Moteurs Electriques a Champ magnetique tour- 
nant. Baudry et Cie., Paris, 1892. 

Hospitalier, E. Polyphased Alternate Currents. Alabaster, 
Gatehouse & Co., London, 1892. (Reprinted from Elec. Review, 
1891, pp. 418, 474, 501, 534, 554, 590, 724.) 

Rodet et Busquet. Les Courants Polyphases. Gauthier-Villars, 
Paris, 1893. 

Kapp, G. Electric Transmission of Energy. Whittaker, London, 
1894 ; also Cantor Lectures at Society of Arts, 1891. 

Arnold, E. Die Theorie und Berechi^ung der asynchronen 
Wechselstrom-Motoren. Seydel, Berlin. (Reprinted from 
Zeitschrift fur Elektrotechnik , 1894, Heft i.-vii.) 

-The Calculation of Alternating Current Motors. Elec. World 

(N.Y.), xxi.-xxiv. 

Snell, A. T. Electric Motive Power. Electrician Series. Lon¬ 
don, 1894. 

Martin, T. C. Inventions, Researches and Writings of Nikola 
Tesla, with special reference to his work in Polyphase Currents 
and High Potential Lighting. The Electrical Engineer, New 
York, 1894. 

Banti, Angelo. I Motori Elettrici a Campo Magnetico Rotatorio. 
Tipografia Elzeviriana, Rome, 1894. 



226 


Polyphase Electric Currents . 


b. MEMOIRS, NOTES, Etc. 

1824- 26 Arago. Ann. Chim. Phys., xxvii. 363, 1824 ; Ann. 

Chim. Phys., xxviii. 325, 1825 ; Pogg. Ann., iii. 343, 
1825 ; Schweigger's Journal, xlvi. 167, 1826 ; Ann. Chim. 
Pliys., xxxii. 213, xxxiii. 223 ; (Euvres Completes (Paris 
edition), iv. 424. 

1825- 32 Sturgeon. [Observations on Magnetic Drag on Disks.] 

Edin. Philos. Journal , July 1825 (Barlow’s Article on 
Sturgeon); Baumgartner's Zeitschrift, i. 138,1826; Philos 
Magazine, April and May 1832 ; Sturgeon’s Scientific 
Researches, p. 211, Bury, 1850. 

1825 Babbage and Herschel. Phil. Trans. Roy. Soc., 1825, 
p. 467. 

1831 Faraday. Explication of Arago’s Magnetic Phenomena. 

Phil. Trans. Roy. Soc., 1831 ; and Experimental Re¬ 
searches in Electricity, i. 24. 

1863 Jochmann, Emil. Ueber die durch Magnetpole in rotirenden 
korperlichen Leitern inducirten elektrischen Strome. 
Physik. Gesellschaft, Berlin, Oct. 1863 and Jan. 1864. 
1876-7 Bielmayr, J. Zur Geschichte des Rotations-Magnetismus. 

Program der kgl. hayer. Studien-Anstalt zu Aschaffen- 
burg. 

1879 Baily, W. A Mode of producing Arago’s Rotations. Philo¬ 
sophical Magazine, Oct. 1879. 

1881. Guthrie and Boys. On Magneto-Electric Induction. Proc. 
Physical Soc., iii. pt. iii. 127, and iv. 55. 

De Fonvielle and Lontin. Nouveau tourniquet electrique. 
LaLum. Elec., ii. 158. 

Hertz, Heinrich. Ueber die Induction in rotirenden Kugeln. 

Inaugural Dissertation. Berlin, March 1880. 

Deprez, Marcel. Synchronisme electrique de deux mouve- 
ments quelconques. Seances de la Soc. Frangaise de 
Physique, Jan.-April 1880, p. 48. 

1883 -Sur le synchronisme electrique de deux mouvements 

relatives et de son application a la construction d’une 
nouvelle boussole electrique Comptes Rendus, 1883, ii. 
1193. 

1884 Smith, Willoughby. Volta- and Magneto-Electric Induc¬ 

tion. Proc. Roy. Institution , June 1884. 



Appendix . 227 

1887 Thomson, Elihu. Novel Phenomena of Alternating Cur¬ 
rents. Amer. Inst. Elec. Engineers, May 1887. 

1888 Duncan, L. Alternating Current Electric Motors. Amer. 
Inst. Elec. Engineers, Feb. 14, 1888. 

Patten, F. J. Discussion of this paper. 

Ferraris, G-. Rotazioni Elettrodinamiche prodotte per 
mezzo di correnti alternate. Atti della R. Accademia 
delle Scienze di Torino, xxiii. p. 360. Pub. Turin, 1888, 
by E. Loescher. An English translation of this memoir 
appeared in Industries , iv. 505, 1888. 

Tesla, Nikola. A New System of Alternate Current Motors 
and Transformers. Amer. Inst. Elec. Engineers , May 
1888 ; La Lum. Elec., xxix. 87 ; Elec. Eng. (N.Y.), vii. 
252 : Industries, iv. 576 ; Electrician, xxi. 173 ; Elec. 
World (N.Y.), xi. 281. 

Swinburne, J. On the Tesla Alternate Current Motor. 
Electrician, xxi. 342. 

[Anon.] The New Westinghouse Motor, &c. Elec. World 
(N.Y.), xii. 222 ; Electrician, xxii. 18. 

Thomson, E., and Wrightman, M. J. Phenomena of Mag¬ 
netic Propagation. Elec. World (N.Y.), xxii. 220. 

1889 Patten, F. J. The Evolution of a New Type of Alternate 

Current Motors, Amer. Inst. Elec. Engineers, Sept. 1891. 
Du Bois-Reymond, A. Arbeitsiibertragung durch Wechsel- 
strom. Elelc. Zeitsch. x. 1. 

1890 Thomson’s Alternate Current Motor. Elec. Review, xxvii. 

77. 

Kennedy’s Alternating Motor, Elec. World (N.Y.), xv. 335 ; 

Elec. Review, xxvi. 462. ^ 

Tesla, N. Moteur a courants alternatifs. La Lum. Elec., 
xxxv. 136. 

_Electromoteur a courants alternatifs decales. Ibid., 462. 

Tesla’s New Alternating Motor. Elec. Review, xxvii. 207. 
Some New Types of Alternate Current Motors (Tesla’s). 
Elec. World (N.Y.), xvi. 101. 

Richard, G. Distribution a courants alternatifs decales de 
Patten. La Lum. Elec., xxxv. 455. 

[Anon.] Moteur a courant induit alternatif de Van Depoele. 
La Lum. Elec., xxxv. 40. 


228 


Polyphase Electric Currents. 


1890 Thomson, Elihu. Alternate Current Motor. Western Elec., 

vi. 354, 360. 

1891 Duncan, L. Alternate Current Motors. Elec. World (N. 

Y.), xvii. 341, 357. 

Hutin and Leblanc. Etude sur les Courants alternatifs, 
&c. La Lum Elec., xl., Nos, 18 to 23. 

-De l’application des courants alternatifs a la Trans¬ 
mission du Travail. Bull. Soc. Internationale des Elec- 
triciens , July and Aug. 1891. 

Von Dolivo-Dobrowolsky, M. Kraftiibertragung mittels 
Wechselstromen von verschiedener Phase (Drehstrom). 
Electrotechniker , 1891, Nos. 4 and 5 ; Elek. Zeitsch., xii. 
149 ; Electrician , xxvii. 388 ; La Lum. Elec. xli. 

-Der Drehstrom und seine Entwickelung. Off. Aus- 

stellung-Zeitung, Frankfurt am Main , 1891. 

-Die Drehstrommotoren der Allgem. Elek. Ges. Elek 

Zeitsch., 1891, 238 ; Electrician, xxvii. 388. 

[Anon.] Oerlikon Three-Phase Alternator. Elec. Review, 
xxvii. 381. 

May, O. High-Pressure Transmission of Power : Experi¬ 
ments at Oerlikon. Elec. World (N. Y.), xvii. 291. 

Stanley and Kelly. Distribution of Power by Alternate 
Currents. Elec. World (N. Y.), xvii. 432. 

-An Unique Mining Plant (Tesla’s Motor). Elec. World 

(N. Y.), xvii. 223. 

Hutin and Leblanc. Alternating Current Motors. Comptes 
Rendus, cxii. 935. 

Goerges, H. Rotary Currents and the Art of Measuring 
them. Elec. Review, xxviii. 506, 517 ; La Lum. Elec., 
xl. 201 ; Elec. Zeitsch ., xii. 213. 

Du Bois-Reymond, A. Einige theoretische und expe- 
rimentelle Untersuchungen fiber Drehstrom. Elec. 
Zeitsch., xii. 303, June 8th, 1891. 

-Translation of above. Deduction and Experiments on 

Rotary Currents. Elec. Review , xxviii. 711 ; Elec. World 
(N. Y.), xvii. 478. 

Hospitalier, E. Alternating Current Motors. Soc. Fran- 
gaise de Physique, July 1891 ; Elec. Review, xxix. 206 ; 
Elec. World (N. Y.), 149 ; Electrician, xxvii. 392. 




Appendix. 229 

1891 [Anon.] C. E. L. Brown’s 20 Horse-power Three-Phase 
Alternate Current Motor. Elec. Review, xxix. 448. 
[Anon.] Haselwander’s Motor. Elec. Zeitsch., 1891,540 ; 

Elec. Anz., 1891, 609 ; Western Elec., viii. 293. 

Stanley and Kelly. Stanley Alternate Current Motor. 
Elec. World (N. Y.), xviii. 266. 

Gutmann, L. The Inventor of the Rotary Field System. 
Elec. World (N. Y.), xviii. 293. 

Pupin, M. I. On Polyphasal Generators. Amer. Inst. Elec. 
Engineers, viii. 562, Dec. 1891 ; Bull. Assoc. Ing. Elec- 
triques , iii. 89. 

Hering, C. Lauffen-Frankfort Power Transmission Plant. 
Elec. World (N. Y.), xviii. 126, 156, 194, 232, 249, 319 
343, 346. 

Kapp, G. The Electric Transmission of Power. Electrician, 
xxvii. 445, 477 ; La Lum. Elec., xli. 336. 

-Lauffen-Frankfort Transmission Plant. Electrician, 

xxvii. 548. 

Perrin. Transformation des courants alternatifs en con- 
tinus et inversement. La Lum. Elec., xxxix. 109. 

Dobrowolsky. Electromoteur. Ibid., 212. 

Kennedy. Electromoteur. Ibid., 306. 

Geraldy, F. Essai d’une theorie simple des machines a 
champ magnetique tournant. Ibid., xli. 7. 

Dobrowolsky. Details sur la transmission par courants 
polyphases. Ibid. xli. 604. 

Sahulka, J. Theorie du champ magnetique tournant de 
Ferraris. Ibid., xlii. 253. 

Sahulka and Dobrowolsky. Dispositifs d’electromoteurs 
a champ magnetique tournant. Ibid., 563. 

De Bast. Electromoteurs a champ magnetique rotatoire. 

Ibid., 527 ; Bull. Assoc. Ing. Electriques, ii. 359. 

[Anon.] Transmission d’Heilbronn a Francfort. L'Elec- 
tricien, i. 279. 

Rechniewski, W. Distribution de l’energie electrique. 
Ibid., ii. 57. 

Brown, C. E. L. Moteurs triphases d’Oerlikon. Ibid., ii. 
189, 365. 



230 Polyphase Electric Currents. 

1891 [Ayrton, W. E.] Three articles on Exhibition at Frankfort. 

Nature, xliv. 615 ; xlv. 54, 105. 

Zickermann , F. Ueber Arbeitsmessung bei Wechselstrom 
mit besonderer Beriicksichtigung des Drehstromarbeits- 
dynamometers von Siemens & Halske. Elek. Zeitsch., 
xii. 509. 

Ayrton, W. E. Note on Rotatory Currents. Electrician, 
xxviii. 178 ; Nature , xlv. 191. 

[Anon.] Priority in Alternating Current Motors. Elec.' 
Eng. (N. Y.), xii. 262. 

Heinrichs. The Multiphase Alternating Current on the 
Frankfort Exhibition (Schuckert’s Machines). Elec. Eng. 
(N. Y.), xii. 273. 

Guttmann. Method of Operating Alternate Current Motors. 
Elec. Eng. (N. Y.), xii. 230. 

Tesla. Electro-Magnetic Motor. Elec. Eng. (N. Y.), xii. 

58 ; see also Elec. Review (N. Y.), xvii. 298. 

Weston, A. H. On the Design of Alternating Current 
Motors. Elec. Review , xxviii. 491. 

Stort. Zur Geschichte der Kraftiibertragung mittels ro- 
tirenden magnetischen Feldes (Riickblick). Elek. Zeitsch., 
1891, 309. 

[Anon.] Vertheilungssystem mittels mehrphasigenWechsel- 
stromes von Haselwander. El. Anz., 1891,609 ; Western 
Elec., viii. 293. 

Du Bois-Reymond, A. Priority in Rotary Current Motors. 

Elec. World (N. Y.), xviii. 74. 

[Anon.] Frankfort Exhibition. Industries, 1891. 
Swinburne, J. Probable Future of Condensers in Electric 
Lighting. Industries , xi. 611. 

1892 Blathy, O. Condensers and Self-induction to Split Phase. 

Z. fiir Elek., x. 1892, p. 366. 

Schilling, G. Ueber Drehstrommotoren. Akad. der Wis- 
sen. in Wien, May 1892. 

Behn-Eschenburg. Three-phase Power. El. Zeitsch.. 1892, 
73. 

Schmidt, A. The Tesla Multiphase Current Motors. Elec. 
Review, xxx. 453. 

V on Miller, O. Elektricitatswerk Lauffen a / N-Heilbronn. 
R. Oldenbourg, Munich. 


Appendix . 231 

1892 Hering, C. Efficiency of the Lauffen-Frankfort Power 
Transmission Plant. Elec. Review, xxxi. 98. 

Hutin and Leblanc. Alternate-current Dynamo-electric 
Motors. Industries, xii. 48. 

Kennedy, Rankine. Electrical Distribution by Multiphase 
Currents. Elec. Review, xxxi. 808. 

-The Induction Motor: Who invented it? Ibid., 515, 

595. 

Reckenzaun, A. Multiphase Transmission and Distribution 
of Energy. Ibid., 552, 599, 789. 

[Anon.] The Schuckert Rotary Field Motor. Ibid., 216. 

-An Instrument for Determining the Phase of Alternate 

Currents. Ibid., 351. 

Stanley, Wm. Alternate Current Motors. Nat. Elec. L. 
Ass. 1892, p. 161. Elec. World (N. Y.), xix. 157. 

Patten, F. J. Proposed System of Alternate Direct Current 
Transformation. Elec. World (N. Y.), xix. 202 ; L'Elec- 
tricien, ii, 252. 

-Self-starting and Self-exciting Synchronous Alternate 

Current Motors. lec. World (N. Y.), xix. 226. 

Hering, C. Transmission of Power with Special Reference 
to the Frankfort Plan. Ibid., 162,'; Nat. Elec. L. Ass., 
Feb. 1892. 

-Mr. Tesla and the Drehstrom System. Elec. World 

(N. Y.), xix. 84. 

Kelly, J. F. Kinematics of the Rotary Field. Ibid., 259. 

Ennis. Development of Divergent-phase Electrical Machin¬ 
ery. Mech. World, May 13. 

Holz, O. Measurement of Lag between Two Alternate Cur¬ 
rents. Elec. World (N. Y.), xix. 216 ; Elec. Review, 
xxxi. 532. 

Horry. Rotating Magnetism obtained from the Alternating 
Current. Elec. World (N. Y.), xix. 243. 

Tesla, Nikola, The “Drehstrom” Patent. Elec. World 
(N. Y.), xx. 222 ; see also 209, 260, 324, 372. 

Steinmetz, C. P. Frequency of Alternate and Polyphase 
Current Systems. Ibid., 150. 

Kelly, J. F. Alleged Superiority of the Three-phase Motor. 
Ibid., 36. 


232 Polyphase Electric Currejits. 

1892 Dobrowolsky. Reply to Attack on Multiphase Current 
Systems. Ibid., 4 ; and see 86. 

Brown, C. E. L. The Inventor of the Three-phase Alter¬ 
nating System. Elec. Eng. (N. Y.), xiii. 85. 

-Comparative Merits of the Two-phase and Three-phase 

Systems. Elec. World (N. Y.), xx. 114. 

[Anon.] Polyphase Motors in America. Ibid., 253. 

Winand, P. A. N. Mechanical Illustration of Polyphased 
Currents. Ibid., 310 ; Journ. Franklin Inst., Oct. 1892. 

Braun, F. Elektrische Kraftiibertragung insbesondere fiber 
Drehstrom. H. Laupp, Tubingen, 1892. 

-Ein Drehstrommotor fiir Vorlesungszwecke. Zschr. 

Phys. Chem. Unterr., v. 189. 

von Miller, O. The Three-phase System in Europe. Elec. 
World (N. Y.), xx. 143, 149. 

Ledeboer. Progres de l’electricite en 1891. [Article con¬ 
taining a history of rotatory field motors.] La Lum. 
Elec., xliii. 7. 

Goerges, H. Recherches recentes sur les moteurs a courants 
alternatifs. Ibid., 124. 

Meissner. Description de la transmission Lauffen-Franc- 
fort. Ibid., xliv. 435, 617 ; Elekt. Zeitschr., xiii. 193. 

Schuckert. Moteur a champ magnetique tournant. Son 
emploi comme transformateur. Ibid., xlv. 23. 

Sahulka, J. Les moteurs a courants alternatifs a champ 
tournant. Ibid., xlvi. 224. 

Lucas, F. Transformation des courants continus en alter¬ 
natifs simples ou polyphases. Ibid., xlvi. 274. 

Wahlstrom. Transformation des courants polyphases. 
Ibid., xlvi. 525. 

Banti, A. Les machines a courants triphases de la maison 
Siemens et Halske de Berlin. Ibid. , xlvi. 674. 

Dihlmann. Distance de transmission des courants de haut 
potentiel. EIndustrie Elec., p. 374 : Elek Zeitsch., 1892. 

Rechniewski, W. Distribution de l’energie electrique. 
L'Electricien (2nd series), iii. 21. 

•-Moteurs a champ tournant. Ibid. , 4. 

--Traitement geometrique des problemes des courants 

alternatifs. Ibid., 401. 



Appendix . 233 

1892 Rechniewski, W. Excitation des dynamos a courants poly- 
phases. Ibid., 256. 

Stanley and Kelly. Alternomoteurs a condensateurs. 
Ibid., 228. 

Yorel. Champ tournant cree par un courant continu. 
Ibid., iv. 416. 

Dieudonne. Transmissions existantes par courants alter¬ 
nates polyphases. Ibid., iv. 39. 

[Anon.J Apparatus of Ducretet and Lejeune. L'Electricite 
xvi. 416. 

Sahulka, J. Ueber Wechselstrommotoren mit magnetis- 
chem Drehfelde. Zschr. fur Elek., 1892, 5, 74, 118. 

-Ueber die Feldstarke der Zweiphasenmotoren mit mag- 

netischem Drehfelde. Elek. Zeitsch., xiii. 119. 

Behn-Eschenburg. Arbeitsmessung bei Dreiphasen Dreh- 
strom. Elek. Zeitsch., xiii. 73. 

Aron, H. Drehstromzahler. Ibid., 193. 

Kollert, J. Beitrage zur Theorie des Drehstromes. Ibid., 
191. 

Weinhold. Drehstrom Lecture-apparatus. Ibid., 300. 

[Anon.] Zur Geschichte des Mehrphasenstroms in Deutsch¬ 
land. Elek. Anzeiger, 1892, 135. 

Farman. Moteur Schuckert a champ magnetique tournant. 
La Lum. Elec., xlv. 23 ; Elec. Review, xxxi. 216. 

Blathy. Alternating Current Motor. Zschr. fur Elek., 
1892, 365. 

Siemens and Halske. Dynamos and Motors. Industries, 
xiii. 312. 

Du Bois-Reymond. Distributing Rotary Current. Elec. 
Review (N. Y.), xx. 243. 

Goerges. Ueber die Ausgiebigkeit der Ankerwickelung 
bei Gleichstrom, Wechselstrom und Drehstrom. Elek. 
Zeitsch., xiii. 236. 

[Anon.] Bradley’s Multiphase Patents. Elec. Eng. (Lond.), 
ix. 494. 

Rotten. Schaltungsweise fur elektrische Drehstromkraft- 
maschinen. Elek. Zeitsch., xiii. 420. 

Heather. Notes on the Production of a Rotating Magnetic 
Field. Electrician , xxviii. 246. 


234 Polyphase Electric Currents. 

1892 Weiler. Ein Apparat fur Wechsel- und Drehstrome. Elek. 

Zeitsch., xiii. 138. 

1893 Reckenzaun, A. Brown’s Non-synchronous Motor for 

Ordinary Alternate Currents. Elec. Review, xxxii. 95. 
Russell, A. Rotary Magnetic Fields. Ibid., 652. 
Kennedy, R. The New System of Alternating Current and 
Transformer Distribution. Ibid., 444, 465, 524, 580, 
608, 635, 661. 

Danielson, E. Reversibility of Three-Phase Motors with 
Inductive Winding. Ibid., 169 ; also Elec. World (N. 
Y.), xxi. 44. 

Deri. Alternate Current Motors. Zeit fur Elek.. March 1, 
1893 ; Electrician, xxx. 630. 

-Starting Alternate Current Motors. La Lum. Elec., 

April 22, 1893. 

Behn-Eschenburg, H. Alternate Current Motors. Elec. 

World (N. Y.), xxi. 353, 372, 424, 458. 

[Anon.] New Stanley-Kelly, Two-Phase Motor System. 

Ibid., 325 ; Elec. Review, xxxii. 740. 

Wahlstroem. Rotary Field from Single-Phase Current. 
Elec. World (N. Y.), xxi. 360. 

Brown, C. E. L. Single-Phase Alternate Current Motors. 
Ibid., 290, 358, 433 ; Elek. Zeitsch., 1893, 81 ; Electrician, 
xxx. 358, 636 ; Elec. World., xxii. 58 ; La Lum. Elec., 
xviii. 113. 

Thomson, E. Single-Phase Alternating Motors. Elec. 
World (N. Y.), xxi. 228, 314. 

Brown, C. E. L. Nicht synchron laufender Motor fur 
gewohnlichen Wechselstrom System. Elek. Zeitsch., 
xiv. 81. 

Dobrowolsky. Reply to Brown. Ibid. , 178 ; and see ibid., 
283 and 285. 

Arnold, E. Non-Synchronous Motors for ordinary Alter¬ 
nate Currents. Elek. Zeitsch., xiv. 256. 

Gutmann, L. Rotary Magnetic Field and Multiphase Alter¬ 
nate Current Distribution. Elec. World (N. Y.), xxi. 276. 

Goerges, H. Regulation of Three-Phase System. Ibid., 123. 
Bradley, C. S. Long Distance Transmission of Power. 
Nat. Elec.L. Ass., March 1893. 


Appendix . 235 

1898 Mascart, E. Moteurs a courants alternatifs. Bull. Soc. 
Internationale des Electriciens, 1893, x. 345. 

Boissonas, A. and J. Travail et rendement des moteurs 
alternatifs asynchrones monophases. La Lum. Elec., 1. 
109. 

Sahulka, J. Theorie der Thomsonschen (Brownschen) 
Motoren fiir ge wohnlichen W echselstrom. Elek. Zeitsch., 
1893, 391. 

Hutin and Leblanc. Transformation des courants alterna¬ 
tifs en courants continus. La Lum. Elec., xlvii. 51. 
Boucherot. La Theorie des machines a champ tournant. 

La Lum. Elec., 1. 151, 220, 524. 

De Bast.. L’Alternomoteur asynchronique monophase de 
Brown. Bull, de VAss. des Ing. Electriciens, August,1893. 
Farman. Theorie des moteurs a flux tournant. La Lum. 
Elec., 1. 317, see also 1. 264. 

Blondel. Theorie elementaire des appareils a champ tour¬ 
nant. La Lum. Elec., 1. 351, 473, 516, 605. 

Kratzert. New Multiphase System. Elek. Zeitsch., May 12. 
Behn-Eschenburg. Theoretisches iiber asynchrone Weeli- 
selstrom Motoren. Elek. Zeitsch., 1893, p. 519. 

Russell, A. Alternating Currents and Rotatory Fields. 

Electrician , xxx. 651, April 7, 1893. 

Ries and Scott. Some Recent Developments in Alternate 
Current Motors. Elec. Review, xxxiii. 583. 

Banti, A. Experiments on Brown’s Asynchronous Motors. 

Elec. Review , xxxiii. 667 ; xxxiv. 60, 114. 

[Anon.] Municipal Central Station at Erding. Elek. Zeitsch., 
1893, Heft. 39. 

Kolben, E. Design of Alternating Current Motors. Elec. 

World (N. Y.), xxii. 284 ; Electrician, xxxi. 590, 618. 
Arnold, E. Long Distance Transmission of Power. Elec. 
World (N. Y.), xxii. 58. 

Snell, A. T. Distribution of Power by Alternate Current 
Motors. Elec. Engineer, xi. 377, 403, 433. 

Olivetti, C. Starting Synchronous Motors. Elec. Review , 
xxxii. 555. 

Kingdon, J. A. Hysteresis Theory of Brown’s Alternate 
Current Motor. Electrician, xxx. 604; see also p. 663. 
Arno, R. Rotatory Electric Field and the Rotations due to 
Electrostatic Hysteresis. Electrician, xxx. 516. 


236 Polyphase Electric Currents . 

1893 Arno, R. Lauffen-Heilbronn Transmission. Ibid ., 353. 

Goerges, H. Debit specifique des induits a courants con- 
tinus et a courants alternatifs simples ou polyphases. 
La Lum. Elec., xlvii. 133. 

Blondel. Mesure de la puissance des courants polyphases. 
Ibid., 139; VElectricien, 2nd series, v. 197. 

Hospitalier, E. Conditions de fonctionnement des moteurs 
a courants triphases. E Industrie Electrique, ii. 12. 

-Moteurs de l’Allgemeine Electricitats Gesellschaft. 

Ibid., ii. 214. 

- Moteurs d’Oerlikon. Ibid., 280. 

Rechniewski. Enroulements des machines electriques. 
EElectricien, 2nd series, v. 21. 

Jacquin. Transport et distribution de l’energie electrique 
par les courants polyphases a Heilbronn. La Lum. Elec ., 
xlviii. 301, 370. 

Dobrowolsky. Les Moteurs a champ tournant de la Societe 
generale d’Electricite de Berlin. Ibid., 328. 

Korda, D. Multiplication du nombre des periodes des cou¬ 
rants sinusoidaux. Ibid., 345. 

Guilbert. Moteurs a courants alternatifs a Oerlikon. 
Ibid., 366. 

-Moteurs a courants alternatifs de MM. Hutin et Leblanc. 

Ibid., 451. 

Kratzert. Systeme a courants triphases. Ibid., 428. 

Korda, D. Mesure des differences de phases de deux cou¬ 
rants sinusoidaux. EIndustrie Elec., ii. 218. 

De Chasseloup-Laubat, G. Notes sur les Courants Alter¬ 
natifs Polyphases. Mem. Soc. des Ingenieurs Civils, 
1893, ii. 168. 

Snell, A. T. Distribution of Power by Alternate Current 
Motors. Inst. Elec. Eng., xxii. 280. 

[Anon.] Application des Courants triphases a la Manoeuvre 
des Ponts roulants. EIndustrie Elec., ii. 259. 

Frolich, 0. Ueber die Messung der Arbeit des Drehstromes. 
Elek. Zeitsch., xiv. 574. 





Appendix. 237 

1893 Ferraris, G. Un metodo per la trattazione dei vettori 

rotanti ed alternativi ed una applicazione di esso ai 
motori elettrici a correnti alternate. Mem. Reale Accad. 
d. Sci Torino , serie ii. tomo xliv., Dec. 3rd, 1893. 

Ferraris, G. Translation of the above. Electrician, xxx iii. 
110, 129, 152, 184. 

Korda, D. Verdoppelung der Periodenzahl und das Messen 
der Phasendifferenz von Weehselstromen. Elek. Zeitsch., 
xiv. 329. 

Von Dolivo-Dobrowolsky. Die neuesten Drehstrommoto- 
ren ohne Schleifkontakte der Allgem. Elek. Ges. Ibid., 
183. 

Behn-Eschenburg. Regulirbarer Wecbselstrommotor. 
Ibid., 300. 

Puluj, J. Messapparat fur Phasendifferenz von Wechsel- 
stromen, &c. Ibid., 686. 

Hutin and Leblanc. A propos du nouveau moteur de M. 
Brown. La Lum. Elec., xlvii. 371 ; Electrician, xxx. 
505. 

[Anon.J Das Elektricitatswerk Lauffen-Heilbronn. El. 
Zschr., 1893, 18. 

[Anon.] Recent progress in the Introduction of the Triphase 
System (Heilbronn, Novorossik, Hartford). Elec. World 
(N. Y.), xxi. 45. 

Forbes, G. The Electrical Transmission of Power from 
Niagara Falls. Journ. Inst. Elec. Eng., xxii. 484. 
[Anon.] Badt’s Multiphase Railway and Lighting System. 
Western Elec., xii. 62. 

1894 Bell, L. Practical Properties of Polyphase Apparatus. 

Amer. Inst. Elec. Engineers, 1894, No. 2 ; Elec. World, 
xxxiii. 334, 367, 400. 

Moler and Bedell. An Optical Phase Indicator and Syn¬ 
chronizer. Amer. Inst. Elec. Engineers , 1894, No. 10. 

Pupin, M. I. Resonance Analysis of Alternating and Poly¬ 
phase Currents. Ibid., No. 10. 

Reber, S. Theory of Two and Three Phase Motors. Ibid., 
No. 10. 

Steinmetz, C. P. Discussion on this paper. Ibid., No. 10. 
Bell, L. Some Facts about Polyphase Motors. Ibid., No. 11. 


238 Polyphase Electric Currents. 

1894 Duncan, L. Experiments on Two-phase Motors. Ibid., 
No. 11. 

Gutmann, L. On the Production of Rotary Magnetic Fields 
by a Single Alternating Current. Ibid., No. 12. 

Bathurst, F. Switzerland as the present Electrical Centre 
of Europe. Elec. World (N. Y.), xxiii. 731, 765, 797, 
829, 859. 

Ferraris, G. On a Synchronous Alternate Current Elec¬ 
tric Motor. Atti di Torino , xxix., April 1st, 1894; Elec¬ 
trician , xxxiii. 101. 

Arno, R. Experiments on Brown’s Alternate Current 
Motor. E Elettricista, iii. No. 7. 

Bell, L. The Saving of Copper in Three-Wire Three-Phase 
System. Elec. Review , xxxiv. 141 ; Elec. World (N. Y.), 
xxiii, 111. 

[Anon.] The First Three-Phase Transmission Plant in the 
United States (Redlands). Elec. Review , xxxiv. 171. 

[Anon.] Three-Phase Transmission Plant in America (Taft). 
Ibid., 593. 

[Anon.] Three-Phase Transformer. Ibid., 426. 

[Anon.] Three-Phase Plant at Concord. Elec. World 
(N. Y.), 364. 

Scott, C. F. Polyphase Transmission. Nat. Ele4. Light 
Assoc., March 1st, 1894 ; Elec. World (N. Y.), xxiii. 358, 
393. 

Patten, F. J. Who Invented the Rotary Field Motor and 
Bi phase System of Power Distribution ? Elec. World 
(N. Y.), xxiii. 283. 

[Anon.] The General Electric Co.’s Three-Phased Appa¬ 
ratus. Ibid., 581. 

Duncan, J. D. E. Proof of Two-Wattmeter Method of Meas¬ 
uring Three-Phase Power. Ibid., 763. 

Friese, R. M. Die Vorgange im Gleichstromanker bei 
Entnahme von Wechsel- und Mehrphasenstromen. Elelc. 
Zeitsch., xv. 101. 

- Alternate Currents from Continuous Currents. Elec. 

World (N. Y.), xxiii. 373, 468, 615. 

Lunt, A. D. Measurement of the Power of Polyphased 
Current. Ibid., 771, 804, 832. 


Appendix . 239 

1894 [Anon.J Stanley Elec. M. Co. Two-Phased System for 
Lighting and Power. Ibid., 815. 

Kennedy, Rankine. Alternate Current Motors. Elec . 
Review, xxxv. 156, 318, 651. 

Esson, W. B. Monophase Motors. Ibid., 317. 

[Anon.] Duncan’s Alternate Current Meter. Elec. Review 
(N. Y.), Sept. 19, 1894. 

Deri, M. Herstellung eines Drehfeldes durch Einphasen- 
Wechselstrome. (One to Three-phase Transformer.) 
Zeitsch. fur Elektr., xii. 377; Elec. Zeitsch. xv. 353; Elec. 
World, xxiv. 82. 

[Anon.] Stanley and Kelly. Alternating Current System. 

Elec. Review (N. Y.), xxiv. 285. 

Behn-Eschenburg. Theory of Alternate Current Motors. 

Elek. Zeitsch., Mar. 29 and May 17, 1894. 

-Polyphase from Single Phase. Elec. Zeitsch., Jan. 1894. 

Boucherot. Transport de force. La Lum. Elec., Hi. 301, 
369. 

-Distribution de force et eclairage par courants poly¬ 
phases aux ateliers Weyher et Richemond. Bull. Soc. 
Intemat. des Electriciens, Dec. 1894. 

Hutin and Leblanc. Transformation reciproque des cou¬ 
rants continus en courants alternatifs, &c. L'Electri- 
cien, April 21st, 1894. 

Steinmetz, C. P. Multiphase Motors. Elek. Zeitsch., Jan. 
25, 1894. 

Potier, A. Sur les Moteurs a induit ferme sur lui-meme. 
Bull. Soc. Intemat. des Elec., May, 1894. 

[Anon.] Imhoff’s New System for Distribution. L'Eel. E., 
i. 688 ; Elek. Zeitsch., xv., 638. 

Blondel, A. Inductance des^ Lignes aeriennes pour cou¬ 
rants alternatifs. L'Ecl. E., i. 393. 

Jullig, Max. Ueber die Gestalt der Kraftlinien eines mag- 
netischen Drehfeldes. Akademie der Wissenschaften in 
Wien , July, 1894. 

Heyland, A. Ein graphisches Verfahren zur Verausberech- 
nung von Transformatoren und Mehrphasenmotoren. 
Elec. Zeitsch., xv. 561. 


240 Polyphase Electric Currents . 

1894 Arno, R. Retardation of the Polarization in Dielectrics, 

Electrician, xxxiv. 327. 

Lahmeyer, W. Regelung von Drehstromanlagen, &c. 
Elek. Zeitsch., xv. 675. 

[Anon.] Polymorphe Generatoren und Transformatoren. 
Ibid., 307. 

Behn-Eschenburg. Vermehrung der Zahl der Erregerpha- 
sen zur Erzeugung rotirender magnetischer Felder. 
Ibid., 35. 

Goerges, H. Ueber das Anlassen der Elektromotoren, 
speciell der Drehstrommotoren. Ibid., 644. 

Kolben, E. Asynchrone Wechselstrommotoren fur hohe 
Spannung. Ibid., 597. 

Stuart-Smith. Instrument for Measuring Phase Difference. 

Elec. World (N. Y.), xxiii. 172. 

Hospitalier. Generateurs et Transformateurs polymor- 
phiques. Soc. frangaise de Physique, May 18, 203. 

Jacquin, Ch. Transmission de force motrice par courants 
polyphases aux ateliers du Jura-Simplon. La Lum. 
Elec., lii. 10, 73. 

1895 De Bast. Discours inaugural. [Theory of Asynchronous 

Polyphase Motors.] Bull. Assoc, des Ingenieurs Electri- 
ciens, vi. 30, March 1895. 

Weinhold, A. Electricitatswerk der Stadt Chemnitz. 

Elek. Zeitsch., 1895, Heft 1 ; Electrician, xxxiv. 464. 
Fischer, L. Berechnung von Mehrphasenstromanlagen. 
Elek. Zeitsch., 1895, Heft 6 and 7. 

Goerges, H. Vergleichende Betrachtungen iiber die Wirth- 
schaftlichkeit des Einphasen- und des Mehrphasen- 
stromes. Elek. Zeitsch., 1895, Heft 3. 

Cahen, H. Zur rechnerischen Bestimmung der Mehrphasen 
Motoren. Elek. Zeitsch., xvi. 52 ; Electrician, xxxv. 265. 

Steinmetz. On Complex Quantities [Mathematical Theory 
applied to Polyphase]. Official Rep. of Proc. of Electrical 
Congress at Chicago, 1893, 68. 

Scott, C. F. On Tesla Polyphase System. Ibid., 417. 

Duncan, L. Multiphase Motors and Power Transmission. 
Ibid., 411. 


Appendix. 241 

Perry, N. W. The Tesla Two-phase System. Electricity 
(U.S.A.), viii. 169, 185. 

[Anon.J Trial of a Tesla Motor. Ibid., May 15. 

[Anon.] The Monocyclic System. Elec. World (N.Y.), xxv. 
182 ; VEcl. Elec. iii. 152. 

Bell, L. The Monocyclic System. Nat. Elec. L. Assoc., 
Feb. 1895 ; Elec. Review (N.Y.), xxvi. 120. 

[Anon.] Niagara To-day. Elec. Eng. (N.Y.), Jan. 15th, 1895. 
Janet, P. Methode dTnscription electrochimique des 
Courants alternatifs. Bull, de la Soc. Internationale des 
Electriciens , Jan. 1895. 

Legrand, L. Calcul d’un moteur asynchrone a champ ma- 
gnetique tournant. EEc. E., Jan. 19th, 1895. 

Julius and Steels. Transport d’energie par courants poly¬ 
phases des carrieres de M. Wincqz, a Soignies, Bull. 
Assoc, des lngenieurs Electriciens , March and April 1895. 
Bragstad. Untersuchung eines Drehfeldes. Elec. Zeitsch., 
xv i. 112. 

Whitwell, A. Theory of Three-phase Generators. Elec. 
Review , xxxvi. 768. 

Eborall, A. C. Single-phase Alternate-current Motors. 

Elec. Review , xxxvi. 722, 738, 789. 

Mershon, K. D. Output of Polyphase Generators. Elec. 
World , xxv. 684. 


APPENDIX II. 


SCHEDULE OF SOME BRITISH PATENTS BEARING 
ON POLYPHASE AND ALTERNATE-CURRENT 
MOTORS. 


No. 

1886 Wynne. II 39 I 

1887 Coerper. . .. 9013 

1888 Tesla. . 6481 

Tesla. 6502 

Goolden, Atkinson & Gold. 16852 

Wilson. 18525 

1889 Thomson, E. 6065 

Tesla. 6527 

Dobrowolsky. io 933 

Tesla. ... 19420 

Tesla. 19426 

Dobrowolsky. I 955 S 

1890 Wenstrom. 5423 

Dobrowolsky. 13260 

Kennedy. 14817 

Kennedy. 16889 

Dobrowolsky. 20425 

1891 Hutin & Leblanc. ... 584 

Dobrowolsky. 3191 

Siemens & Halske. 8151 

Stanley & Kelly. 95 22 

Siemens & Halske. 10612 

Siemens & Halske. 10613 

Tesla. 11473 

Sahulka. 12046 




























Appendix. 


243 


1891 Dobrowolsky. . 13503 

Brain & Arnot. 13627 

Bradley, Taylor & McDonald. 16099 

Tesla. 16709 

Siemens & Halske. 1S890 

Stanley & Kelly. 20604 

1892 Siemens & Halske. 360 

Stanley & Kelly. 7504 

Siemens & Halske. 13543 

Hutin & Leblanc. 13765 

Stanley & Kelly. 14056 

Swinburne. 16919 

Oerlikon Co. 20505 

Brown. 21811 

Arnold. 23290 

Brown. 23902 

Brown. 23961 

Brown. 24098 

1893 Rice. 510 

Bradley. 1621 

Lundell & Johnson.. . . 5339 

Lundell & Johnson. 534 ° 

Duncan. 6241 

Hutin & Leblanc. 12139 

Hutin & Leblanc. 12458 

Kingdon. 14664 

Swinburne. 16307 

1894 Ries Electric Co. 3986 

Bradley. 4 J 7 ° 

Bradley. 4 H 1 

Ferranti. 6458 

Coerper. 7239 

Blondel & others. 8638 

Mordey. 9605 

Rowland. iio 59 

Kelly & Stanley. 12875 

Langdon-Davies. 19364 

Clark. 20241 

Siemens & Halske. 21141 









































244 


Polyphase Electric Currents. 


No. 

1895 Devonshire (for Gen. El. Co.). 2914 

Devonshire “ “ 2915 

Devonshire “ “ 2916 

Devonshire “ “ 2917 

Devonshire “ '* 2918 

Ferraris and Arno. 11227 







INDEX. 


References are in many cases given in footnotes in the text; when not so given 
the original source may be found in the Bibliography (Appendix I.). Names in 
the Bibliography are also for convenience included in the Index , even in cases 
where the bibliographical entry is a mere reference. 


A. 

PAGE 

Advantages of Polyphase Generators. 21 

Allgemeine Elektricitats-Gesellschaft , Frankfort Transmission.. 105 , 106 

“ “ “ Motors, Efficiency of. 205 

“ “ “ Inductor Generators. 220 

Alternate Currents. 2 

Alternating Current into Continuous. 182 

Alternating Magnetic Fields combined... 59 

“ “ “ Experiment with . 154 

“ Vectors. 161 

Alternator {see Generator). 

“ Simple. 2 

Ampere's Experiments on Rotating Disk. 7 1 

Amplitude.... . 8 

Analytical Theory of Motors. 146 

* Angle of Lag {see Lag). 

Angular Spacing of Polyphase Fields. 60 , 64 

“ Speed.*. *34 

Apparent Watts. *6 

Arago , Francois, his Rotations. 69 , 226 

Armature {see Rotor). 

Arno , R . 235 , 236 , 237 , 239 

“ Efficiency Tests by. 208 

“ his Patent on Electrostatic Hysteresis. 235 

Arnold , E .*43, 225 , 234 , 235 

Aron , Dr. H., Polyphase Meter. . 189 , 220 

“ “ on Measurement of Power. 233 

Atkinson's Motors. *73 

Auto-transformer. x 85> 221 

Ayrton , IV. . . 2 3° 






























246 


Polyphase Electric Currents . 


B. 

PAGE 

Babbage and Herschell, Experiments on Magnetic Rotations. 71 , 226 

Bacelli, Experiments on Magnetic Rotations. 7 1 

Back Electromotive-force.I44> I 5 2 > I 9° 

“ “ “in Monophase Motor. 169 

D., Multiphase Railway Project. 237 

Baily, Walter, First Induction Motor. 84 , 226 

Baltimore Station. 224 

Banti, A . 225 , 232 , 235 

Barlow's Experiments on Compass Needle. 69 

Bast, De, Theory of Monophase Motors. . 159 , 229 , 2 35> 2 4° 

Bathurst, F . 237 

Bedell, F. . 237 

“ “and Ryan . 171 

Behn-Eschenburg . 230 , 233 , 234 , 235 , 237 , 238 , 239 

Bell, Dr. Louis . 237 , 240 

“ “on Starting Torque. 199 

“ “ on Constancy of Speed. 202 

“ “ on Weight of Motors. 209 

Bellegarde, generators at. 39 

Bielmayr . 226 

Bilboa, Plant at. 185 

Blakesley, T. H., “ Alternating Currents of Electricity ”. 10 

Blondel, A . 171 , 239 

“ and others, Patent of. . 243 

Blathy, 0 . 230 , 233 

Bockenheim, Plant at. 220 

Boissonnas, A. and J . 235 

Bois-Raymond, A. du . 227 , 228 , 230 , 233 

Borel's Motor. 90 

Boucherot . 215 , 235 , 238 

“ Efficiency Tests by. 208 

Boys, C. Vernon (see also Guthrie and Boys') . 226 

Bradley, C. S . 234 

“ “ his Polyphase Work. 91 

“ “ his Motors. 92 

“ “ his Patents. 91 

“ “ Transformer. 184 

Brags tad . 241 

Braun . 232 

Breadth-Coefficient. 25 

Breadth of Coil. ... . 23 , 25 

Breadth of Iron of Stator. 133 

Breitenburger . 216 

Bremgarten, generators at. 39 















































Index . 247 

PAGE 

Brown , Boveri & Co ., Alternators of. 35 

“ “ “ Motors of. 211 et seq. 

Brown , C. E. L . 229 , 232 , 234 

“ “ Designs Eauffen Generators. 27 

“ “ Designs Hochfelden Generators. 39 , 211 

“ “ Introduces “ Umbrella ” Type of Machine. 37 

“ “ liis Designs for Niagara Plant. 39 

* Experiments on Motor Design.. 118 , 119 

his Embedded Conductors. 32 

“ Method of arranging Coils. 25 

“ “ his Rotor. 117 

“ his Patents. 243 

“ his Monophase Motors. 157 

“ “ his Starting Gear. 201 

“ “ Efficiency of his Motors. 208 

Budapesth, Station at. 185 

Busquet and Rodet . 225 


C. 

Cohen , H . 240 

Capacity.. H 

“ used to Split Phase. *5° 

Central Stations, Polyphase. 217 

Centrifugals, for Sugar Refineries. 216 

Chasseloup-Laubat, De . 2 3 ^ 

Chemnitz, Station at. 218 

Chesney (see Stanley-Kelly). 

Characteristic Curve of Motor.. J 4 2 

“ “ Monophase Motor. 163 , 164 

Choking-coils. J 5> I ^» 221 

Christie , P., Experiments on Magnetic Rotations. 7 1 

Circuits in Rotor. I2 3 

Clock-diagram. 13 , 24 , 26 , 46 

Clark's Patent . 243 

Coerper's Motor. 9 1 

“ Rotor. 122 

“ Patent.... 242 

Coil for producing Rotatory Field. 81 

Coils, Breadth of. 23 ’ 25 

‘ ‘ Overlapping of. 33 

Colladon, Experiments on Magnetic Rotations. P 

Combinations of Electromotive-forces. 45 










































248 Polyphase Electric Currents . 

PAGB 

Combinations of Polyphase Currents. 43 > 49 

“ of Magnetic Fields. 5^ 

Common Return, Use of. 

Commutator for Imitating Three-phase Currents. 79 « 8° 

Concord, Plant at.. 22 4 

Condenser, Electrolytic. J 57 

Condensers used in Starting. 174 

Conductors imbedded in Iron... 32 

“ in Motor, Length of.191 et seq. 

“ in Rotor. 115 et seq., 122 

Constancy of Speed. 202 

“ of Magnetic Flux. 135 

Continuous Current transformed into Alternating.... 182 

Copper, Saving in, by Use of Polyphase. . 53 

Core-disks. .32, 113 

Core of Polyphase Transformers.177, 179, 180 

Counter Electromotive-force. . 144, 152, 169, 190 

Crane Motors. 198 

Crank Mechanism.61, 62 

Currents in Rotor.116, 147 et seq., 196 

“ “ of Monophase Motor.164, 165 

Current in Stator.151, 152, 190 

Curve, Characteristic, of Motor. 142 

“ “ Monophase Motor.163, 164 


D. 

JDanietson , Experiments with Asynchronous Generators.42, 234 

De Bast (see Bast). 

Depoele , van . 227 

Deprez , Marcel , on Combination of Two Alternating Fields. 60 

“ “ Researches of. .87, 226 

Deri , Max. .234, 238 

Design of Motors. 190 

Developed Winding. 6 

Development of Polyphase Motor. 84 

Diagram for Efficiency of Motors. 136 

Dieudonnk . 233 

Difference of Phase. .11, 18, 20, 222 

Dihlmann . 232 

Direction of Induced Currents.4^ TI 6 

Distribution of Polyphase Currents. 217 

Dobrowolsky (see below). 








































Index. 


249 


Dolivo-Dobrowolsky , M. von .228, 229, 232, 234, 236, 237 

“ “ on Comparative Output of Machines... 21 

“ “ Researches. 102 

“ “ “ Motors.102, 107 

M “ “ Patents.242, 243 

*' “ “ Rotor. 122 

“ “ “ Three-phase Lamps. 53 

*' “ “ on Variation of Field. 132 

Drehstrom...62, 102, 106 

Drum-winding of Stator.127, 128 

Du Bois-Reymond , A .227, 228 

Duncan , Dr. Louis .143, 227, 228, 237, 240 

“ J. D. E . 238 

“ 71 , Motor. 174 

“ “ Polyphase Meter. 189 

“ “ Patent. 243 


E. 


Ebert , Construction of Lauffen-Frankfort Line. 107 

EberalL , A. C . 241 

Economy of Copper. 53 

Eddy-currents. .69, 73, 116 

Efficiency of Lauffen Plant .31, 32 

“ Lauffen-Frankfort Transmission.109, no 

“ Motors... 202 

“ Rotor.i 35 > 150 

“ “ Diagram of. 136 

Egg- S pinning in Rotating Field. 82 

Electrolytic Condenser. 1 57 

Electromotive-force in Alternator Coils.23, 25 

“ “ Counter.144, 152, 169, 190 

“ -forces in Rotor. JI 6, 123, 136 


Electrostatic Hysteresis... 

Elliptical Rotation. 

Elliptically Rotating Current in Monophase Motor 
“ “ Field in Monophase Motor.. 


235 . 239 
,... 61 
.... 168 
.... 168 


Emperor Wilhelm II. contributes to the Lauffen-Frankfort Trans¬ 
mission . 

Ennis , C. F. . . 

Equalizing Three-phase Circuits. 

Esson , W. . . 

Experiments with Rotating Magnetic Field. 








































250 


Polyphase Electric Currents . 


P. 

PAGE 

Faraday's Discovery of Induction Currents.2, 226 

“ Researches in Magnetic Rotations.72, 75 , 226 

Fartnan .233, 235 

Ferraris, Prof. Galileo, Researches of.88, 143, 227, 236, 237 

“ “ “ Theory of Monophase Motors ... 161 

“ “ “ Patent of. .243 

Ferranti- Wright Motor. . 172 

Field-magnet.16, 29 

Fischer, L .. 240 

Fleming, Prof. J. A ...10, 155 

Flux-density in Motors. 132 

Flux-phase. 177 

Fonvielle (and Lontin ), Continuously Rotating Copper Disk... 76, 226 

Forbes, Prof. George, Niagara Scheme. 39 

“ “ “ on Niagara Transmission. 237 

Force on Iron, rather than on Copper. 33 

Force on Rotor. 116 

Foucault's Experiment on Rotating Disk. 75 

Frankfort Exhibition. 103 

Frankfort-Lauffen, Transmission of Power between.27, 106 

Frequency, Number of Poles, and Speed.115, 192 

Friese . 238 

Frolich, O . 236 


G. 

Gambey's Observation on Compass Needle. 

Ganz's Motors. 

General Elec. Co. ( U. S .), Asynchronous Generators 


Generator. I} 

“ Single-phase Elementary. 2 

“ “ Westing house . 4 

“ Polyphase. 16 

“ “ Asynchronous. 42 

“ “ Bellegarde. 39 

“ “ Bremgarten. 39 

“ “ Brown's .32. 35 . 37 , 42 


“ Brush Co's ( Mordey) 

“ Gordon's . 

“ Gramme's . 






































Index. 


25 1 

PAGE 

Generator, Polyphase, Hochfelden. 39 

“ “ Lauffen . 27 

“ “ Lontin’s . 17 

“ “ Niagara. 39 

“ “ Oerlikon Co.’s .33, 39 

“ “ Schonenwert. 37 

“ “ Stanley . 35 

“ “ “ Umbrella ” Type. 37 

“ “ Westinghouse .34, 40 

“ “ Wynne’s . 19 

Geraldy , F. . 229 

German Emperor contributes to Lauffen-Frankfort Transmission... no 

Geerges, H .21, 57, 228, 232, 233, 234, 236, 239, 240 

“ “on Copper required in different Systems. 57 

“ “on Comparative Output of Machines. 21 

“ “ on Equalizing Pressures. 221 

Goolden & Co.’s Motors. 173 

“ “ Patent. 242 

Gordon ^ J. E. H., Two-phase Alternator. 19 

Grouping of Rotor Conductors. .122 et seq. 

Gramme’s Alternator. 17 

Gramme-ring Transformer. 180 

Guilbert . 236 

Guthrie and Boys . 226 

Researches with Rotating Magnets. 75 

Gutmann , L .229, 230, 234, 237 


H. 

Haselwander’s Motors.. 100 

Heat produced in Rotor. *49 

“ “ Stator. I 5 I 

Heather . 2 33 

Heilbronn, Electric Lighting of. 27, 217 

Heinrichs . 2 3 ° 

Helios Co.’s Motors. 9 L 112 

“ “ Monophase Motor.. 158 

“ “ Transformers. *84 

Hellsjon, Plant at. 221 

Hering , Carl . 22 9 > 2 3 r 

Hertz , Prof. H, Researches on Rotating Spheres.74, 226 

Herschel ( see Babbage and Herschel ) 

Heyland. . 239 

Hochfelden, Plant at. 39 . 2n 










































252 Polyphase Electric Currents . 

PAGB 

Holes in Core Disks. 32, 36, 113, 119, 195 

Holz , O . 231 

Horry . 231 

Hopkinson , Dr . John . 17 1 

Hospitaller , Prof. E .225, 228, 236 

“ “ on Polymorphic Machines. 185 

Hutin and Leblanc .143, 228, 231, 235, 237, 238 

“ “ Patents of.242, 243 

“ “ Theory of Monophase Motor.161 

“ “ Transformer. 184 

Hysteresis, Law of. . 132 

“ Electrostatic.235, 239 


I. 

Imhoff. . 224 

Impedance. 13 

Impressed Field.131, 138, 146, 150, 159 

Independent Circuits in Rotor. 123 

“ Windings. 44 

Inductance.. 11, 12 

Inductor ( see Stator). m 

“ Type of Generator.35, 174, 220 

Intermediate Phases. 103 


J. 

Jacquin .236, 241 

Janet . 241 

Jochmann . 74, 226 

Julius . 241 

Jiillig . 239 


K. 

Kapp, Gisbert. ..223 229 

“ “ “ Alternate Current Machinery ”. IO 

“ “ on Plant Efficiency of Motors. 209 

“ “ on Theory of Motors. . 

Kelly (see Stanley and Kelly) .228, 229, 231 


































Index. 


2 53 


Kennedy , Rankine .229, 231, 234, 238 


“ “ Alternating Motor. 227 

“ “ Patents of. 242 

Kingdon, J. A . 235 

“ his Patent... 243 

Kittler , Dr. ,Experiments on Lauffen-Frankfort Transmission. no 

Killwangen, Plant at. . 211 

Kolben, Emil . .235, 239 


“ on Starting Torque. 198 

“ Table of Efficiencies. 203, 204 


Kollert . 233 

Korda,Dksirt, Transformer.182, 236, 237 

Kratzkart .235, 236 


L. 


hag . 

Tag of Resultant Flux. 

Lahmeyer, W . . 

Lahmeyer & Co.'s Machines. 

Lamps, Combinations of. 

“ Tri-wick. 

Langdon-Davies's Motor. 

“ “ Patent. 

Lap-winding. 

Lauffen, Plant at. 

“ Three-phase Generators at 
Lauffen-Frankfort Transmission... 
Lead. 


11, 13 , 45 , 155 , 169 
. 138 

. 239 

.104, 184, 220 

. 5i 

. 53 

. 175 

. 243 

. 6 

. 217 

. 27 

. 106 

. 11, 14, 46 


Leblanc (see Hutin and Leblanc). 

v 2\2 

Ledeboer . 

Legrand, L . 2 '^ 1 

Le Roux's Experiment on Copper Disk. 75 

Lindlev, W. H., Experiments on Lauffen-Frankfort Transmission.. no 

Liquid Resistances. I98, 220 

Loss of Energy in Rotor. 35 

“ “ in Stator. 


Lucas , F. . 

Lundel & Johnson's Patents 

Lunt . 


232 

243 

238 







































*54 


Polyphase Electric Currents . 


M. 


PAGB 

Magnetic Field, Combination of. 58 

“ “ Progression of. 129 

“ “ Rotation. 7 ° 

‘ ‘ Magnetism of Rotation ”. 7 1 

Magnetomotive-force of Coils. 129 

Martin , T. C. . 225 

Marsh's Experiments on Compass-needle. 69 

Mascart , Prof. E. . 235 

Matteucci's Experiments on Magnetic Rotations. 74 

May, O . 228 

Maximum Flux Density. 133 

Maxwell's Eaw of Periodic Currents. 14 

Measurement of Phase-difference...236, 240 

Measurement of Polyphase Power. 187 

Mechanical Illustration of Polyphase Transmission. 82 

Mechanical Performance of Motors. 197 

Meissner . 232 

Mesh Connection, Power in. 1S7 

Mesh-groupings. 43 

Meters for Polyphase Currents. 189 

von Miller, Oskar .217, 220, 230, 232 

“ “ engineers the Lauffen Transmission. . 106 

Model of Polyphase Transmission. 83 

Moler . 237 

Monocyclic System. 221 

Monophase Motors. 153 


“ “ Currents in Motor of.164,165 

“ Starting of.156,199 

Mordey , W. M., on Synchronous Motors. 171 

“ “ Alternating Motors. 174 

Motors, Analytical Theory of. 7 146 

Motor as Revolving Transformer. hi 

Motor Design. 190 

Motor, Efficiency of. 202 

Motors, Miscellaneous. 170 

“ Monophase. 153 

“ Modern Examples. 210 

“ of Allgemeine Elek. Ges .216 

“ of Atkinson . 173 

*' of Baily . 84 

“ of Borel .. 90 

“ of Bradley . 92 
















































Index. 


255 


Motors of Brown , Bovert & Co. 

“ of Coerper . 

“ of Deprez . 

“ of Dobrowolsky . 

“ of T. Duncan . 

“ of Ferranti and Wright. 

“ of Ferraris . 

“ of Ganz & Co . 

“ of Haselwander . 

“ of Helios Co . 

“ of Langdon-Davies . 

“ of Mordey . 

“ of Oerlikon Co . 

“ of Shallenberger . 

“ of Tesla . 

“ of El. Thomson . 

of Wenstrom . 

“ of Westing house Co .... 

“ Requirements of. 

“ Speed of. 

“ Starting of. 

4 4 Structure of Polyphase. 

44 Theory of. 

44 Weights of. 


PAGE 

... 157, 211 

. 91 

. 87 

. . . . 102, 107 

. 174 

. 172 

. 88 

. 175 

. 100 

.158 

.175 

. 174 

157. 207, 210 

. 173 

• • • 93 et seq. 

. 172 

. 102 

. 216 

. 197 

.... 191, 202 

. 197 

. hi 

. 134 

. 209 


N. 


Niagara, Generators at. 39 

Nobili's Researches on Magnetic Rotations. 71 


O. 

Oerlikon Co's Three-phase Generator .. 

“ “ Machines. 

“ <f List of Stations equipped 

“ “ Monophase Motor. 

“ 44 Patents of. 

“ “ Starting Gear. 

Olivetti , . . 

Oppositely Rotating Vectors. 


• 33 . 39 
105, 106 
.... 221 

.... 157 

.... 243 
.... 200 
.... 235 
.... 162 




































256 


Polyphase Electric Currents . 


P. 

PAGE 

Paccaud and Borel's Meter. . . . 90 

Pantin, Plant at. 208 

Patten .227, 231, 238 

Period. 7 

Periodicity. 7 

Peripheral Speed. 191 

Perrin . 229 

Perry , N. IV . 240 

Phase.8, 18 

Phase-difference. 223 

“ ** Measurer.236, 239, 240 

“ “ of Rotor and Stator Currents. 138, 140, 141, 151 

Phases, Intermediate. 103 

“ of Combined Currents. 49 

Phase-splitting.88, 98, 156, 175, 200 

Phase-transformation. 179 

Picou , R. V. .171, 225, 143 

Pitch. 6 

“ of Poles.. 6 

Pittsfield, Plant at. 221 

Poisson on Magnetism of Rotation. 71 

Poles, Number of, on Motor. 192 

Polyphase Generators. 16 

“ Systems, Method of Connections.43 et seq. 

Ponemah Mills, Plant at. 171 

Potier , A . 239 

“ “ Theory of Motors. 146 

Power, Polyphase. 187 

Prtvost, Experiments on Magnetic Rotations. 71 

Primary Winding of Motor. hi 

Progression of the Field. 129 

Properties of Rotating Magnetic Fields. 69 

Puluj , J .. - - ... 237 

Pupin, M. I . .229, 237 


Q 

Quadrature. 20 

Quarter-period. 19 






































Index . 


2 57 


R. 

PAGE 

Reactive Effect.n, 12 

Reber. .143, 237 

Rechnie7vski ...229, 232, 233, 236 

Reckenzaun. A .231, 234 

Regulation of Three-phase Circuits.218, 220 

Repulsion of Conductor in Alternating Field. 154 

Resistance in Rotor, Introduction of.125, 140, 198 

“ “ Effect of. 197 

Resultant Magnetic Flux.134, 137, 146 

“ of several Magnetic Fields. 58 et seq. 

Retardation of Polarity. 173 

Rice's Patent. 243 

Ries . 235 

Ries Electric S. Co. ’s Patent. 243 

Rhodes, W. G . 171 

Rodet and Busquet . 225 

Rotatory Magnetic Fields.20, 58 et seq., 69 

“ “ “ Experiments with. 76 

Rotation of Conductor in Alternating Field. 155 

Rotatory Electric Field.235, 239 

Rotating Vectors. J 6i 

Rotor, Definition of. II2 , 113 

“ Design of. *94 

“ Different Forms of. !20 

“ Structure of. II 3 > XI 5 

‘‘ Experimental. 11 9 

“ Winding of. 122 

Rotten . 2 33 

Rowland's Patent. 2 43 

Russell . 2 34 > 2 35 

Ryan (see Bedell and Ryan). 


S. 


Sahulka, Dr. J . 

St. Etienne, Plant at. 

Scalars, Combinations of... 

Schilling . 

Schluss-anker . 

Schmidt, A . 

Schonenwert, Generator at 

Schuckert . 

17 


143, 225, 229, 232, 233, 235 

. 211 

. 67 

. 230 

. 116 

. 230 

. 37 , 215 

. 232 








































258 Polyphase Electric Currents . 

PAGB 

Schuchert & Co.'s Machines. 104 

“ “ Transformers.179, 184 

Schwenger's Sugar Refinery. 216 

Scott, C. F ..235, 238, 240 

“ “ Two- to Three-phase Transformer... 181 

Secondary Coils of Transformer.176, 180 

Winding of Motor.111 

Seebeck, Researches on Magnetic Rotations. 71 

Self-Induction, Effect of. 3 

“ “ used to Split the Phase. ... 89, 98, 150 

Self-starting Synchronous Motors. 171 

Sellers, Coleman, Niagara Generators. 39 

Series, Conductors in. 122 

Siemens & Halske . 233 

“ “ equip Chemnitz Station. 217 

“ “ Machines at Frankfort. 105 

“ “ Patents of.242, 243 

“ “ Transformers. 178 

“Similars”. 122 

Sine curve.7, 8, 9 

“ “ Flux as a. . 131 

Sine Function, Effect of Deviation from. 65 

“ “ Combinations of.. 68 

Single-phase Alternate Currents. 2 

“ “ (see Monophase). 

Shallenberger's Motor.. 173 

Polyphase Meter. 189 

Slip. 135 

Slippage. 135 

Slip-rings for Insertion of Resistance. 125 

Smith , Willoughby . 226 

“ “ Researches on Rotating Metal Disks. 75 

Snell, A. T. .225, 235, 236 

Spacing, Angular, of Polyphase Fields.60, 64 

Speed of Motor. 191 

“ Constancy of. 202 

Spiral Winding. 5 

Splitting the Phase.88, 98, 156, 175, 200 

Squirrel-cage.102, 116, 118, 122 

Stanley.228, 229, 231, 233 

Stanley's Two-phase Generator. 35 

Stanley-Kelly Motors. 173 

“ “ Patents of.242, 243 

Star Connection, Power in. 188 

Star-Groupings . 43 

Starting of Motors..156, 197, 200 
















































Index. 


259 


Starting Gear. 

“ of Monophase Motors.. 

“ Resistance, Insertion of. 

“ Torque. 

Stator Breadth. 

“ Definition of. 

“ Design of. 

“ Structure of. 

Steels . 

Steinmetz, C. P. . 

“ “ Monocyclic ” System. 

“ Theory of Motors. 

“ on Hysteresis. 

Stuait-Smith . 

Stort . 

Sturgeon, W ., his Experiment on Moving Disk 

Strassburg, Station at. 

Synchronism and Asynchronism. 

Synchronous Motor .. . 

“ Motor versus Asynchronous. 

“ Polyphase Motors.... . 

Swinburne, J . 

“ Patent of... 


PAGE 

. 200 

. 150 , 199 

.125, I40, I43 

. 139 

. T 33 

. 112 

. IX 9> I 9° 

. 113. !27 

. 240 

171, 231, 237, 239, 240 

. 221 

. 143 , 144 

. 132 

. 240 

. 230 

.72, 74, 226 

. 220 

.112, 205 

. 17 

. 205 

. 170 

.227 

. 243 


T. 


Tesla, Nikola .227, 230, 231 

“ “ Researches of.93 et seq. 

“ “ Patents of.93, 100, 242, 243 

“ “ Designs of Rotors. 120 

“ “ Transformer. 84 

“ “ Motors of Westinghouse Co. 216 

“ “ Test of. 209 

Theory of Polyphase Motors.134, 146 

“ of the Monophase Motor.. 158 

“ of Thomson's experiment. . 155 

Thomson, Prof. Elihu .227, 228, 234 

“ “ “ Experiment of. . 154 

“ “ Motor of.150, 156, 172 

“ “ “ Patents of.. 242 

Three-wire System, Employing Difference of Phase .. 223 

Three-phase Generators.21, 27, 220 

“ Power. *87 

“ Systems, Method of Connections. 43 













































26 o 


Polyphase Electric Currents . 


PAGB 

Three-phase System, Saving in Copper in. 53 

“ Transformers. 177 

Torque .136, 148 et seq. 

“ and Slip. 141 

*• represented by Area of Triangle. 138 

“ at Starting. 198 

“ of Monophase Motor.163, 168 

Tramways at Dublin. 185 

Transformer. 176 

Motor condensed as a.ill, 135, 137 

Rotating. 183 

“ Df Dobrowolsky. 103 

Three- to Two-phase.180, 181 

One-to Two-or Three-phase. 182 

Three-phase from Continuous Current. 18 

True Watts. 16 

Two-phase Coils, Winding of. . 129 

‘ ‘ Generator.. 19 

“ Systems, Method of Connections.43 et seq. 

“ Transformers.176, 178 

“ Station at Baltimore. 224 

“ with Three Wires.45, 50 


U. 

‘ Umbrella ’ ’ Type of Machine. 27 


V. 

Variation of Field.^2 

Vector Combination. 67 

Vectors, Alternating and Rotating. x6i 

Vertical Shaft Type of Generator. .. 27 

Virtual Amperes and Volts. IO 


W. 


Wahlstrom . 

Wangen, Plant at 
Walker , G. T... 


232, 234 
.... 211 
••• 155 

































Index. 


261 


PAGE 

Wattless Current. 16 

Watt-meters. 189 

Wave Winding. 6 

Weber, Prof. H. F., Report on Lauffen-Frankfort.106, 109 

Weights of Motors. 209 

Weiler . 234 

Weinhold, A., Lecture Apparatus. 233 

Wenstrdm . 221 

“ his Motors. 102 

Westinghouse Single-phase Alternator. 34 

“ Two-phase Generator. 34 

Weston , A. H . 230 

Weyher and Richemond's Plant.208, 215 

Whitwell, A . 241 

Wilson*s Motor. 102 

“ Patent. 242 

Winand . 232 

Winding of Generators . 35 > 3 ^ 

“ of Rotor. I22 > 195 

“ or Stator. I2 7 

“ Spiral, Lap and Wave. 5 » 6 

Wright and Ferranti's Motor. J 7 2 

Wrightman , M.J. . 22 7 

Wynne , Frank , his Polyphase System. 19 

“ his Patent. 2 4 2 


Y. 

Yorel . . 233 


Z. 


Zeuner's Diagram 
Zickermann, F... 


9 

230 


































Plate i 


2-PHASE ALTERNATE CURRENT MOTOR 6 H. P. 1200 REVS. PER MIN. 

System C. E. L. Brown. 

Scale 1 to 4. 






















































































































































































































































































































































































































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